A P HYSICS -AWARE F RAMEWORK FOR S HORT-T ERM GPU P OWER F ORECASTING OF AI DATA C ENTERS
arXiv:2605.04074v1 [cs.LG] 14 Apr 2026
A PREPRINT Mohammad AlShaikh Saleh1 , Sanjay Chawla2 , Sertac Bayhan3,4 , Haitham Abu-Rub1,3 , and Ali Ghrayeb1 1 College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar 2 Qatar Computing Research Institute, Hamad Bin Khalifa University, Doha, Qatar 3 Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, Doha, Qatar 4 Department of Electrical & Electronic Engineering, Gazi University, Ankara, Turkey
(a) Throttle-aware forecasting. PI-DLinear captures GPU power throttling after the forecasting boundary with lower error than DLinear (MAE/RMSE: 0.4454/0.5103 vs. 0.4703/0.5528).
(b) Transient recovery performance. (c) Post-throttle stability. After throttling subsides, PI-DLinear maintains stable Under abrupt load fluctuations, PI-DLinear recovers forecasting accuracy predictions with lower error than DLinear (MAE/RMSE: 0.1112/0.1469 vs. more robustly than DLinear (MAE/RMSE: 0.1795/0.2274). 1.4650/2.3061 vs. 2.5082/2.8610).
Figure 1: Comparison of DLinear and PI-DLinear across power throttling, transient recovery, and post-event stability regimes. PI-DLinear consistently achieves lower prediction error, enabling accurate throttling characterization, faster recovery from sudden AI load changes, and stable forecasting behavior.
A BSTRACT AI data centers experience rapid fluctuations in power demand due to the heterogeneity of computational tasks that they have to support. For example, the power profile of inference and training of large language models (LLMs) is quite distinct and big divergences can result in the instability of the underlying electricity grid. In this paper we propose, to the best of our knowledge, the first physicsinformed DLinear time-series model that can accurately forecast power utilization of an AI data center 5-80 minutes (short-term forecasting) into the future. The physics, based on a multi-node lumped thermal resistance-capacitance (RC) network consistent with Newton’s law of cooling, is captured using newly derived time-dependent ordinary differential equations (ODE) that separately models and interlinks power consumption with the GPU compute and memory utilization and temperature. The resulting model, that we refer to as PI-DLinear, trained and evaluated on a real AI data center dataset and is not only more accurate than the state-of-the-art (SOTA) models tested, but the forecast profile respects the underlying physics under power throttling and load transient events. Relative to the SOTA transformer-based and non-transformer-based models, improvements in forecasting accuracy (averaged across all look-back and prediction windows) range from 0.782%–39.08% for MSE, 0.993%–51.82% for MAE, and 0.370%–22.28% for RMSE. Keywords AI data centers, DLinear, energy-efficient computing, Physics-aware modeling, power forecasting, power grid resiliency, RC thermal modelling, and transformers.
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
1
Introduction
1.1
Problem Statement
A PREPRINT
The data center industry is rapidly growing, fueled by the rising demand for cloud services, advancements in Artificial Intelligence (AI) and Machine Learning (ML), and the need for data storage. This surge is anticipated to significantly increase global electricity demand related to AI, influenced by a variety of technological, economic, and societal factors Lin and Chien [2023]. This decade has witnessed substantial investments from major tech hyperscalers in expanding data center infrastructures worldwide Mark Haranas [2024], Dan Swinhoe [2024]. However, these escalating demands present challenges for power grids, raising concerns about their ability to accommodate high-density power loads, as noted in PJM’s report on overloaded lines and increasing electricity costs Aurora Energy Research [2024]. Environmental pressures are also prompting data centers to adopt modular designs and renewable energy sources. Moreover, AI-driven data centers are experiencing unprecedented power densities per rack, leading to significant transitory power fluctuations similar to those caused by Electric Vehicles (EVs) and renewable energy systems Lin et al. [2024]. Recently, with large data centers consuming tens to hundreds of megawatts, power changes of several megawatts can occur within mere seconds, potentially disrupting grid frequency control and necessitating faster frequency regulation responses. Notably, modern AI workloads demand much higher power densities, ranging from 300 W to 1,200 W per GPU, and they exhibit rapid power fluctuations, such as exceeding 132 kW/s at the rack level with NVIDIA’s GB200 NVL72 Schneider Electric and NVIDIA [2023]. In light of this, one of the crucial ways to enhance grid reliability is to forecast data center power consumption to inform control strategies such as primary control, secondary control, tertiary control, and Automatic Generation Control (AGC), especially when grappling with substantial power transients driven by AI loads, harmonics, and frequency fluctuations Li et al. [2024]. Additionally, predicting upcoming voltage sags and swells in power consumption can aid AGC in effectively preparing for rapid ramp-up events. Therefore, accurate short-term forecasts of AI data-center demand help grid operators schedule balancing actions and reserve requirements and make real-time network operational decisions more efficient, improving reliability and lowering operating costs. From a grid-planning perspective, short-term forecasts also make it easier to treat data centers as flexible loads (e.g., shifting or curtailing demand through demand response), which can reduce peak stress, avoid/defer costly grid upgrades, and reduce the gap between generation capacity and load demand. Thus, power forecasting continues to be a significant area of research, contributing directly to both improved energy management and system optimization. In recent times, transformer-based (deep learning) models have revolutionized time series forecasting by effectively capturing both short-term and long-term dependencies. To evaluate these advanced models, the Time Series Library (TSLib) Wu et al. [2023] was used, a comprehensive library featuring state-of-the-art (SOTA) models, most of which are transformer-based. Nevertheless, the problem with deep learning models in general is that they can lead to physically inconsistent predictions and are less reliable outside the range (out-of-distribution) of the training data, especially in the event of power throttling, abrupt load fluctuations and AI workloads, and post-throttle stability. These are all cases that our proposed model, which we call physics-informed-DLinear (PI-DLinear), addresses as observed in Fig. 1. Therefore, our paper integrates the first physics-informed framework that guides the model with scientific principles, improving generalization, interpretability, and robustness by anchoring the learning to real physical mechanisms rather than just patterns in the training data for power forecasting across diverse AI workloads (LLMs, vision networks, and GNNs) and multiple temporal historical and prediction scales. The proposed model was tested on the MIT supercloud dataset Samsi et al. [2021], which, to the best of the authors’ knowledge, is the only publicly available dataset demonstrating the impact of AI workloads on data center power consumption. Physics-informed neural networks (PINNs), a field also referred to as scientific machine learning, integrate datadriven and physics-driven approaches to address challenges in science and engineering Raissi [2018], McClenny and Braga-Neto [2023]. These algorithms leverage substantial prior knowledge in the form of algebraic and/or differential equations describing the relationships among variables, making them particularly well-suited for power forecasting applications. However, the problem is that no time-dependent ODE/PDE was available that takes into account the interlink of power consumption with GPU temperature and utilization and memory temperature and utilization, which is a prerequisite to construct a physics-aware framework. Consequently, this is also the first work that required to derive new ODEs using a coupled two-node resistance-capacitance (RC) thermal network to enable their smooth integration as physics-informed constraints for power forecasting in AI data centers. 1.2
Contributions
To this end, the main contributions are as follows: 2
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
• We present the first Physics-Informed DLinear (PI-DLinear) model that incorporates a multi-node lumped thermal RC network, consistent with Newton’s law of cooling, for GPU power forecasting across diverse AI workloads (LLMs, vision networks, and GNNs) along with a systematic evaluation across multiple temporal scales, with look-back windows of 240, 360, 480, and 600 minutes and prediction horizons of 5, 10, 20, 40, and 80 minutes ahead. • To the best of our knowledge, this is the first work that needed to derive new ODEs using the coupled two-node RC thermal network to enable their smooth integration as physics-informed constraints for power forecasting in AI data centers, especially given the limited number of high-importance features in the dataset used. Specifically, the ODEs relate the GPU power to GPU temperature and the memory power to memory temperature, allowing for the modeling of GPU and memory as coupled thermal nodes. • Detecting and predicting power throttling using the proposed PI-DLinear was achieved, delivering improved transient recovery forecasting performance under abrupt AI load fluctuations and stable predictions even after power throttling subsides. • A comprehensive comparison against SOTA transformer-based and non-transformer-based forecasting models demonstrated improvements in prediction accuracy (averaged across all look-back and prediction windows) ranging from 0.782%–39.08% for MSE, 0.993%–51.82% for MAE, and 0.370%–22.28% for RMSE. • The code is provided, allowing researchers to replicate, use, and extend the work for further advancements in power forecasting of AI data centers. 1.3
Related Works
Current research Amvrosiadis et al. [2018], Blöcher et al. [2021], Wilkins et al. [2024] explores various energy-related factors such as workloads and failure rates. However, even diverse datasets with unknown job profiles complicate prediction efforts. As noted in Wang et al. [2024], there are opportunities in reinforcement learning that could enhance scheduling efficiency. Energy management for GPUs is addressed in Rossi and Brunelli [2015], Meisner et al. [2009], focusing on optimizing power based on active or idle states and predictive modeling. Moreover, regression techniques, including Auto Regressive Integrated Moving Average (ARIMA) and fault tree methodologies, are utilized in Shoukourian and Kranzlmüller [2020] to forecast power consumption and failure incidents in data center facilities. Furthermore, Wilkins et al. [2024] investigates how user behavior influences energy usage, while Bai et al. [2022] showcases a convolutional neural network (CNN) approach that improves predictions of GPU power consumption for large language models (LLMs) over traditional methods like ARIMA. Additionally, a Deep Neural Network (DNN) is introduced in Patel et al. [2024] to estimate the computational costs of LLM training in cloud environments. Given the dynamic demands of AI and high-performance computing workloads, accurate short-term power forecasting in data centers is crucial Hu et al. [2021]. Traditional models like ARIMA often fall short in recognizing complex patterns within high-dimensional datasets, while LSTM, GRU, and CNN models demonstrated strong performance in handling these challenges, particularly on the MIT dataset Mughees et al. [2025]. Deep learning techniques stand out for their ability to decipher intricate data patterns, offering promising solutions to the limitations mentioned above Yao et al. [2024]. In particular, recurrent neural networks (RNNs) and their long short-term memory (LSTM) variants have garnered significant attention for their effectiveness in time-series forecasting Aslam et al. [2021]. LSTMs adeptly tackle the vanishing and exploding gradient issues typical of RNNs, enabling them to capture long-range dependencies in time-series data Hossain and Mahmood [2020]. Furthermore, bidirectional LSTM (BiLSTM) networks enhance predictive accuracy by leveraging both past and future contextual information Li et al. [2023]. However, recently, transformers have emerged as the leading architecture for sequence modeling, showcasing exceptional performance across a range of applications, including natural language processing (NLP), speech recognition, and computer vision. Recently, their use for analyzing time-series data has gained traction, as discussed in Wen et al. [2023]. Key transformer-based models for time-series forecasting include LogTrans Li et al. [2019], Informer Zhou et al. [2021], Autoformer Wu et al. [2021], Pyraformer Liu et al. [2022], Triformer Cirstea et al. [2022], and FEDformer Zhou et al. [2022]. The main working power of transformers-based forecasting models is from their multi-head self-attention mechanism, which has a remarkable capability of extracting semantic correlations among elements in a long sequence. Conventional transformer-based time-series forecasting models predominantly assume numeric, particularly continuous, inputs and therefore often overlook recurring motifs that are fundamental to many real-world temporal dynamics. In addition, the widespread strategy of segmenting long sequences into fixed-size sliding windows for supervised training restricts the model’s ability to exploit global contextual information beyond the current segment. 3
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
2
Proposed Forecasting Framework
2.1
Task Definition: Short-Term Power Forecasting
A PREPRINT
We study short-term forecasting of data-center electricity load under AI workloads (e.g., inference bursts and training interruptions). For multivariate time series forecasting, given historical data X = {x1 , x2 , . . . , xL } ∈ RL×C , where L denotes the look-back window length and C is the number of co-variates, xt = [x1t , x2t , . . . , xC t ] represents the multivariate observation at time step t, which includes hardware utilization signals and thermal sensors (GPU utilization, memory utilization, GPU temperature, memory temperature) and the power draw. The objective is to predict the future power consumption sequence y = {PL+1 , PL+2 , . . . , PL+T } ∈ RT over a forecasting horizon of length T , where Pt denotes the power consumption at time step t. Overall, the forecasting task can be formulated as a mapping RL×C → RT , where the input consists of C > 1 variables over L time steps and the output is the power forecast over T future time steps. It is worth noting that the input variables are commonly treated as multiple channels. Our forecasting target is the power consumption Pt (in Watts). Given a look-back window of length L and a forecasting horizon T , we define Xt−L+1:t = [xt−L+1 , . . . , xt ] ∈ RL×C , yt+1:t+T = [Pt+1 , Pt+2 , . . . , Pt+T ]⊤ ∈ RT .
(1)
We learn a forecasting model fθ (Transformer or non-Transformer) that predicts future power, written as bt+1:t+T = fθ (Xt−L+1:t ) ∈ RT . y
(2)
The standard supervised objective minimizes a prediction loss Lpred over N training samples as N
min θ
1 X b (n) , y(n) , Lpred y N n=1 T
(3)
2 1 Xb Lpred (b y, y) = Pt+k − Pt+k , T k=1
where Pbt+k denotes the k-step-ahead predicted power and θ is the learnable parameter that includes the weights and biases of the neural network. 2.2
DLinear
DLinear combines a decomposition approach inspired by Autoformer and FEDformer with linear layers Zeng et al. [2023]. It begins by decomposing the historical time series data into a trend component via a moving average kernel and a seasonal/remainder component. Then, two separate one-layer linear layers are applied to each component, and their outputs are summed to yield the final prediction as Hs = Ws Xs ∈ RT ×C ,
Ws ∈ RT ×L ,
(4)
Ht = Wt Xt ∈ RT ×C ,
Wt ∈ RT ×L ,
(5)
b = Hs + Ht , y
(6)
where Hs and Ht denote the output values of the single-layer linear networks corresponding to the residual and trend components, respectively. Ws and Wt symbolize the single-layer linear networks associated with the residual and trend components, as further shown in Fig. 2. It is worth noting that if the dataset’s variables have different characteristics, i.e., different seasonality and trends, then sharing weights across the co-variates may not perform as desired. Hence, by explicitly addressing the trend, DLinear enhances the basic linear model’s performance, especially in datasets exhibiting clear trends Zeng et al. [2023]. 2.3 2.3.1
Physics-Aware Regularization via a Compact Thermal RC Model Derived ODEs using the Thermal Circuit RC Model
Power consumption and temperature evolution are coupled through energy conservation and Newtonian cooling. Following compact thermal modeling, we adopt a lumped-parameter RC network with two coupled thermal states: GPU temperature Tg (t) and memory temperature Tm (t). We also have Ta denoting the effective ambient/sink temperature. 4
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
Linear Ws Remainder Component
Xs
Hs
LC
T C
Look-back Window
X
Forecasting Output
LC
yˆ
Linear Wt
Trend Component
Xt
LC
Ht
P̂
d dt
2 dP 1 d Tg 1 1 dTg 1 dTm = C g 2 + + − dt dt Rga Rgm dt Rgm dt
T C
1 N LData = | Pˆ − P |2 N i=1
1 N Lr = | P |2 N i=1
Lthrottle = Lhigh + Lstress
LTotal = u LData + r Lr + LThrottle
T C
Figure 2: PI-DLinear Architecture. The base DLinear model (top) decomposes the input look-back window X ∈ RL×C into seasonal/remainder (Xs ) and trend (Xt ) components, which are independently projected to the b ∈ RH×C , from forecast horizon via linear layers Hs and Ht , then summed to produce the full multivariate forecast Y H b ∈ R is extracted. Our physics-informed extension introduces three loss components: which the power channel y (1) Ldata : standard MSE loss with ground truth, (2) Lr : coupled RC thermal network residual enforcing consistency between predicted power and observed temperatures T g , T m , and (3) Lthrottle : utilization-based constraint encoding that high GPU/memory utilization should precede power reduction. The RC parameters for the aggregate GPU rack (Cg = 5.408 × 106 J/K, Cm = 5.481 × 106 J/K, Rga = 2.037 × 10−3 K/W, Rma = 2.055 × 10−3 K/W, Rgm = 6.064 × 10−4 K/W, Ta = 27◦ C, α = 0.5085) are pre-estimated via RLS using the training data and then are kept fixed for validation and testing.
In this paper, the lumped-parameter model is used to simplify a spatially distributed system by representing it as discrete nodes with uniform properties, where each node (e.g., GPU, Memory) has a single temperature value rather than a continuous temperature field. Instead of solving partial differential equations (PDEs) that describe how temperature varies across every point in space, we derive ODEs that describe how the temperature of each lumped node evolves over time. The lumped assumption can be made here because GPUs are designed with high thermal conductivity (copper heat spreaders, thermal paste), so the temperature distribution is relatively uniform within each component, validating the lumped-parameter approximation approach. Applying Kirchhoff’s Current Law at each thermal node (see B.4 for the full derivation), the energy-balance ODEs for the GPU and memory nodes are Tg − Ta dTg Tg − Tm = αP − Cg − , (7) dt Rga Rgm Cm
Tm − Ta dTm Tg − Tm = (1 − α) P − + , dt Rma Rgm
(8)
where Cg , Cm > 0 are the thermal capacitances (heat storage) of the GPU and memory respectively, Rga , Rma > 0 are the thermal resistances from each component to the ambient, Rgm > 0 is the thermal coupling resistance between the GPU and memory, and α ∈ [0, 1] is a latent power split parameter defined below. The terms (Tg − Ta )/Rga and (Tm − Ta )/Rma correspond to Newton’s law of cooling in lumped form (i.e., heat loss proportional to temperature difference). Solving Equation (7) for P and differentiating with respect to time yields the following power rate constraint: dP 1 d2 Tg 1 dTg 1 dTg dTm = Cg 2 + + − , dt α dt Rga dt Rgm dt dt
(9)
where the memory temperature derivative dTm /dt is itself governed by Equation (8), thereby coupling both thermal nodes into the constraint. The thermal capacitance and resistance terms are empirically determined using recursive least squares (RLS), a common practice in thermal RC modeling. We acquire the derivatives of the proposed PI-DLinear model (surrogate model) with respect to time t through chain rule and differentiating function compositions by automatic differentiation (AutoDiff) Raissi [2018], Braga-Neto [2024]. It is worth noting that GPUs convert nearly 99% of electrical energy into heat through transistor switching losses, resistive losses in interconnects, and leakage currents. Also, since the ambient temperature Ta was not provided, it was assumed that due to cooling, Ta was kept constant at room temperature (the minimum observed temperature, which was ≈ 27◦ C). Here, we observe only the total power P (t) rather than its partition into GPU and memory contributions. We therefore introduce a latent split parameter α ∈ [0, 1] as Pg (t) = α P (t),
Pm (t) = (1 − α) P (t).
In practice, α can be treated as a learned scalar or a learned function of workload features. 5
(10)
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
2.3.2
A PREPRINT
Power Throttling Constraint
GPU power throttling is an automatic protection mechanism that reduces power consumption to prevent thermal damage when the processor approaches critical operating limits. In light of this, we observe from the MIT Supercloud dataset that throttling events, characterized by sudden power drops exceeding 15%, are strongly correlated with sustained high utilization rather than extreme temperatures alone, as the critical GPU temperatures (see Fig. 3) never reach the limits 80◦ C − 90◦ C outlined in the product brief NVIDIA Corporation [2018]. This physical insight motivates our throttling-aware loss function, which ensures that when utilization exceeds threshold θU ≈ 90%, power should not increase, i.e., Ut > θU ⇒ ∆P̂t ≤ 0, and simultaneously high temperature and high utilization strongly indicate imminent throttling, i.e., (Ut > θU ) ∧ (Ttg > θT ) ⇒ ∆P̂t ≤ 0. We also set θT to be at the 95th percentile, even though we don’t reach the 80◦ C − 90◦ C limits, yet, the rise in the temperature is highly correlated with the rise in the utilization. These constraints are combined into a single differentiable loss as Lthrottle = Lhigh + Lstress , (11) where each component is penalized, given that it violates the corresponding physical constraint set. Therefore, we have X 1 max(0, ∆P̂t )2 , Lhigh = H −1 t: Ut >θU (12) X 1 Lstress = max(0, ∆P̂t )2 , H −1 g t: Ut >θU , Tt >θT
(g)
(m)
where H is the prediction horizon, ∆P̂t = P̂t+1 − P̂t is the predicted power change, Ut = α · ut + (1 − α) · ut the weighted GPU-memory utilization, and θU , θT are the utilization and temperature thresholds respectively. 2.3.3
is
Loss Function Formulation
The weighting parameter λ, which controls the trade-off between data loss and physics loss along with the hyperparameters of the PINN model, is optimized by obtaining a minimum of the subsequent weighted loss function Braga-Neto [2020] L = λu · LData + λr · Lr + λθ · Lthrottle , (13) through different optimization methods like stochastic gradient descent, Adam, adaptive gradient descent, RMS Prop, etc. Braga-Neto [2020]. The weights λu (data weight), λr (residual weight), λθ (throttle weight) are carefully selected to keep training balanced among the three losses. In this study, the weights are self-adaptive and are therefore updated by gradient ascent in log-space to keep them positive, i.e. ηu = log λu , ηr = log λr , ηθ = log λθ and η ← η + γ∇η L while clipping η to [λmin , λmax ] to avoid instability and collapse to extremes. We also compute Lr during training merely on the sequence length using the observed Tg and Tm so they are rolled out using the learned RC model driven by the predicted future power P̂ . In the proposed algorithm, the weighting factors are considered to be scalar, and thus, the PINNs weight loss function is adhered to in the training optimization process and can be written as N
u 2 . 1 X P̂i (xiu , tiu ; Φ) − Pi , LData (λu ) = Nu i=1
N
(14)
r . 1 X Lr (λr ) = |P (xir , tir ; Φ, ϕ)|2 . Nr i=1
where λu , λr , and λθ are the weights for the data, physics (residual), and power throttle components, respectively, Lu is the data loss component at the collocation points, Lr is the physics (residual) loss component, Lθ is the power throttling loss component Nu , Nr , Nθ are the collocation points, xi represents the i-th collocation point of the co-variates in the 5-dimensional feature space, ti is the corresponding time coordinate feature, P̂ (xiu , tiu ; Φ) is the DLinear prediction at the collocation points (xiP , tiP ), and ui is the actual measurement in the dataset.
3
Experimental Results and Discussion
This brings us to the following questions. 1. Does adding a physics-based constraint to the loss function improve the power forecasting performance for AI-centric data centers? 2. What is the computational burden on running the proposed physics-aware model? 3. What impact does the physics weighting/regularization factor λ have on the power forecasting performance? 4. Can PI-DLinear still perform in the event of power throttling? 6
1000
20
Power (kW)
1500
30
count
Power (kW)
40
40
1000
30
750 500
20
500 10
250
10 0
50 GPU utilization (%)
A PREPRINT
100
count
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
40 60 GPU temperature (°C)
800
60
600
50
400
count
GPU temperature (°C)
(a) Power vs. utilization (left) and power vs. temperature (right).
40 200 30 0
50 GPU utilization (%)
100
(b) Temperature vs. utilization.
Figure 3: Relationships observed in the MIT Supercloud dataset: power vs. utilization (left), power vs. temperature (right), and temperature vs. utilization (bottom). Lighter regions indicate higher count, and darker regions indicate lower count. 3.1
Data Collection and Pre-Processing
The gathered data encompasses GPU power consumption, often the largest portion of total power used in AI workloads, along with metrics like memory utilization, GPU temperature, and storage. Following data collection, the raw data undergoes pre-processing steps, such as Min-Max normalization and data slicing, to prepare it for integration into the forecasting models. In this study, we address the data center power consumption forecasting problem using a real-world dataset from the MIT Supercloud Samsi et al. [2021], a high-performance computing (HPC) system (GPU: Nvidia Volta V100, CPU: Intel Xeon Gold 6248). It is worth noting that, to the best of the authors’ knowledge, this is the only publicly available dataset demonstrating the impact of AI workloads on data center power consumption. The dataset spans February to October 2021 and includes 100-millisecond interval logs of GPU/CPU utilization, scheduling details, and physical critical parameters like power draw, temperature, and utilization plotted in Fig. 3. Key GPU metrics include power, memory, utilization, and temperature, with anonymized user data organized by job ID and node. Aggregated GPU power consumption peaks at 45 kW across 448 GPUs. The dataset details workload composition, dominated by vision networks (e.g., U-Net: 1,431 jobs; VGG, ResNet, and Inception follow), language models (e.g., BERT: 189 jobs; DistillBERT: 172 jobs), and graph neural networks (SchNet, DimeNetm, PNA, and conv) as shown in Fig. 4. Pre-processing maintains a 1-minute granularity, with power consumption aggregated by job ID and node to reflect total power drawn from the local distribution system. After normalization via a min-max scalar, the data uses different look-back windows to predict different prediction lengths in minutes ahead. 7
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
Table 1: Summary of the MIT Superclouddataset used in this study. Attribute
MIT Supercloud GPU Trace 7 (GPU utilization, memory utilization, free memory, used memory, GPU temperature, memory temperature, power draw) ∼330,500 1 min ∼238 days
Co-variates # Timesteps Granularity Duration
This dataset summary (Table 1) indicates that the experiments are conducted on a high-resolution, long-duration multivariate operational trace from the MIT Supercloud GPU cluster. After pre-processing the data, seven variates were sampled at 1-minute granularity, yielding approximately 330k timesteps spanning about 238 days, which is well-suited for evaluating both short-horizon and longer-horizon forecasting under realistic AI workload variability. At the end, 5 co-variates were chosen (omitting memory used and memory free due to low observed correlation), namely the memory utilization (in %), memory temperature, GPU utilization (in %), GPU temperature, and the power drawn. These features were all used for the proposed model along with the SOTA benchmark models. 3.2
Model Training
In time-series forecasting, various deep learning architectures can be utilized, but this paper focuses on 16 state-ofthe-art models renowned for their effectiveness with sequential data, namely, Transformer, iTransformer, TimeXer, TiDE, TSMixer, Reformer, PatchTST, Nonstationary transformer, LightTS, FiLM, FEDformer, Pyraformer, DLinear, Crossformer, NLinear, and Linear. Each model is trained, its hyperparameters are fine-tuned, and validated for performance evaluation. The dataset was preprocessed to ensure consistent formatting, remove missing or corrupted entries, and choose the high-importance co-variates Bak et al. [2025]. Each variable was normalized using Min-Max normalization according to the training set statistics. Then the top model is selected to see the effect of adding the physics constraints on the forecasting performance at different sequence and prediction lengths. 3.3
Forecasting Results
Table 2 shows a clear separation between lightweight linear MLP baselines (DLinear/PI-DLinear) and the majority of transformer variants across all four history/sequence lengths.
Number of jobs
Firstly, the performance is remarkably stable as the history window grows from 240 to 600 minutes for the strongest methods. DLinear varies only slightly (MAE: 0.1420 → 0.1439; MSE: 0.1556 → 0.1576), indicating that the signal required for short-to-mid horizon forecasting is largely captured within a few hours of context. The same stability holds for TiDE and FiLM (e.g., FiLM MAE stays ≈ 0.143 − 0.144 with MSE ≈ 0.157 − 0.158), suggesting that extending history for this dataset diminishes the performance once the recent operating regime is observed.
600 500 400 300 200 100 0
560 463
Model family
Vision Networks (Total: 1507) LLMs (Total: 361) GNNs (Total: 171)
484
189
172 39
27
32
BERTistilBERTDimeNet SchNet D Models Deployed
PNA
Conv
33
VGG ResNetnception I
Figure 4: Computational job distribution across the AI workloads present in the MIT Supercloud dataset, namely, vision networks, large language models (LLMs), and graph neural networks (GNNs). 8
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
Table 2: Average performance across prediction horizons L ∈ {5, 10, 20, 40, 80} min for multivariate forecasting on MIT Supercloud under different history lengths (T ∈ {240, 360, 480, 600} min) for the proposed and baseline models. It is apparent that the proposed PI-DLinear model not only outperforms the baseline models in terms of performance, but it (the error values) is relatively stable as the sequence length increases (see Fig. 5) as well, a feature that is crucial when deploying such a model in data center control units, where multi-scaling and model flexibility is required at any given history and time step. The models were tested with 5 seeds, yet the standard deviation across runs for all models was negligible. T = 240 min Model
T = 360 min
T = 480 min
T = 600 min
MAE
MSE
MAPE
RMSE
MAE
MSE
MAPE
RMSE
MAE
MSE
MAPE
RMSE
MAE
MSE
MAPE
RMSE
iTransformer 0.1481 Transformer 0.1670 TimeXer 0.1474 TiDE 0.1422 TSMixer 0.1507 Reformer 0.1739 PatchTST 0.1495 Nonstationary 0.1489 Transformer LightTS 0.1496 FiLM 0.1432 FEDformer 0.2164 Pyraformer 0.1498 DLinear 0.1420 Crossformer 0.1491 NLinear 0.1673 Linear 0.1463 PI-DLinear 0.1420 (Ours)
0.1636 0.1722 0.1580 0.1561 0.1605 0.1700 0.1628
1.1323 1.2211 1.1021 1.0628 1.0999 1.2483 1.1203
0.4000 0.4095 0.3941 0.3912 0.3968 0.4077 0.3993
0.1527 0.1726 0.1631 0.1436 0.1547 0.1730 0.1520
0.1665 0.1674 0.1664 0.1578 0.1654 0.1666 0.1599
1.1603 1.4009 1.2364 1.0743 1.1798 1.3543 1.1443
0.4039 0.4058 0.4053 0.3933 0.4030 0.4054 0.3959
0.1533 0.1754 0.1511 0.1441 0.1549 0.1693 0.1522
0.1694 0.1727 0.1637 0.1585 0.1657 0.1759 0.1631
1.1537 1.3291 1.1139 1.0708 1.1491 1.2455 1.1335
0.4071 0.4115 0.4014 0.3943 0.4036 0.4166 0.3999
0.1555 0.1785 0.1636 0.1451 0.1640 0.1860 0.1558
0.1708 0.1747 0.1674 0.1584 0.1697 0.1775 0.1645
1.2052 1.3318 1.2195 1.0860 1.2085 1.5094 1.1635
0.4087 0.4140 0.4065 0.3941 0.4082 0.4158 0.4016
0.1736
1.1044
0.4136
0.1505
0.1752
1.1388
0.4159
0.1527
0.1674
1.1212
0.4061
0.1580
0.1702
1.2052
0.4100
0.1668 0.1571 0.2013 0.1610 0.1556 0.1564 0.2080 0.1600
1.1490 1.0708 1.7254 1.2292 1.0403 1.1437 2.0779 1.0771
0.4052 0.3925 0.4478 0.3986 0.3907 0.3925 0.4505 0.3965
0.1526 0.1437 0.2747 0.1531 0.1426 0.1833 0.1460 0.1468
0.1639 0.1577 0.2549 0.1594 0.1561 0.2650 0.1592 0.1603
1.1687 1.0810 2.3160 1.2034 1.0484 2.3161 1.1018 1.0863
0.4010 0.3931 0.5044 0.3959 0.3913 0.5084 0.3952 0.3969
0.1539 0.1440 0.3028 0.1555 0.1434 0.1504 0.1472 0.1479
0.1669 0.1578 0.2976 0.1647 0.1571 0.1579 0.1606 0.1614
1.1695 1.0840 2.5071 1.1664 1.0516 1.1648 1.1004 1.0834
0.4052 0.3934 0.5455 0.4032 0.3925 0.3948 0.3969 0.3983
0.1563 0.1440 0.2741 0.1710 0.1439 0.1535 0.1480 0.1482
0.1691 0.1582 0.2669 0.1822 0.1576 0.1628 0.1602 0.1611
1.1749 1.0877 2.2863 1.5822 1.0646 1.1889 1.1144 1.0906
0.4079 0.3938 0.5151 0.4179 0.3931 0.3995 0.3965 0.3979
0.1546
1.0315
0.3895
0.1429
0.1549
1.0358
0.3899
0.1434
0.1559
1.0414
0.3910
0.1439
0.1561
1.0510
0.3914
Note: Bold indicates the best (lowest) value and underlined indicates the second-best (lowest) value for each metric (normalized).
Second, PI-DLinear (ours) is consistently the strongest across the error metrics and history lengths, with the most consistent gains appearing in MSE/RMSE, which is typically the most sensitive to costly spikes as shown in Table 2. In fact, PI-DLinear achieves the best MSE at every sequence length (0.1546, 0.1549, 0.1559, 0.1561 for 240/360/480/600 min), and correspondingly the best RMSE (≈ 0.3895 − 0.3914), which is further substantiated by the forecasting results observed in Fig. 1. For MAE, PI-DLinear remains tied with DLinear at 240 min (0.1420) and stays within a very small margin of the best thereafter (e.g., 0.1430 at 360 min, 0.1434 at 480 min), while still reducing squared-error measures. This behavior is consistent with the physics term acting as a regularizer that suppresses high-variance deviations without over-smoothing the median error.
360 0.734 0.830 0.953 1.159 1.506
1.50
480 0.735 0.839 0.955 1.182 1.515 600 0.738 0.847 0.961 1.183 1.478 5 10 20 40 80 Prediction Horizon (minutes)
1.25 1.00 0.75
(a) MAPE values.
240 0.099 0.122 0.152 0.187 0.213
0.25
360 0.099 0.123 0.152 0.188 0.216
0.20
480 0.099 0.123 0.153 0.189 0.217 600 0.100 0.124 0.153 0.189 0.216 5 10 20 40 80 Prediction Horizon (minutes)
MSE
1.75
Sequence Length (minutes)
240 0.723 0.835 0.952 1.187 1.496
MAPE
Sequence Length (minutes)
In light of this, PI-DLinear encodes a mechanistic state-space model for the data center’s thermal subsystem, where GPU and memory temperatures are treated as physical state variables whose evolution must satisfy energy conservation plus Newtonian cooling in a coupled lumped RC network (Equation (9)). This turns forecasting into a constrained dynamical inference problem, where the predicted power trajectories are only acceptable insofar as they adhere to a physically realizable temperature response governed by the thermal capacitances/resistances, rather than arbitrary temporal patterns. To this end, because the trace observes total power P (t) but not its GPU/memory split, introducing the latent partition α (Equation (10)) makes the model implicitly perform system identification of how workload power
0.15 0.10
(b) MSE values.
Figure 5: PI-DLinear forecasting results shown as heatmaps for input sequence length T ∈ {240, 360, 480, 600} min and prediction length L ∈ {5, 10, 20, 40, 80} min. PI-DLinear prediction error is stable for different sequence lengths and a shorter prediction horizon is more accurate than longer prediction horizons. 9
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
is allocated across the thermal components, guiding the learned forecast to an interpretable physical decomposition rather than purely statistical smoothing. Moreover, in Fig. 5, it is apparent that the proposed PI-DLinear prediction error seems to be independent of the sequence length and a shorter prediction horizon is more accurate than longer prediction horizons, which is expected as the error accumulates as we predict further in time. Nevertheless, such stability (as the sequence length increases) is a crucial feature of the proposed model, especially for deploying it in data center control units, where multi-scaling and model flexibility are required at any given history and time step. A third takeaway concerns model efficiency vs. accuracy trade-offs, where several complex architectures do not translate their capacity into better average forecasting error on this workload. For example, iTransformer/TimeXer/PatchTST yield MAE values ranging ≈ 0.149 − 0.156 and MSE ≈ 0.160 − 0.171 depending on the sequence length, consistently behind the proposed PI-DLinear and baseline DLinear model. Meanwhile, FEDformer is a clear outlier with substantially larger errors, especially at longer histories (e.g., MAE 0.2747–0.3028 and MAPE > 2.3 for 360–600 min), suggesting mismatch during short-term, high-variability dynamics of GPU traces. Furthermore, Crossformer exhibits a similar instability at 360 min (MSE 0.2650, MAPE 2.3161), even though it recovers at 480–600 min, highlighting that some architectures can be sensitive to the context/sequence length horizons selected. Overall, the results support a simple conclusion aligned with the paper’s message: physics-aware linear forecasting offers a strong robustness prior for AI data center GPU power/thermal proxies. PI-DLinear performs the best relative to the strongest SOTA baselines, while systematically improving the forecasting performance across all history/sequence lengths, which is precisely the regime that matters when avoiding large prediction misses under abrupt AI workload shifts and periodic maintenance activities. The motivation for physics-aware forecasting is also brought about in this case to show that GPU power traces exhibit constrained, regime-dependent behavior driven by device management. In particular, many compute-intensive V100 jobs operated near a tight maximum-power band around the nominal power class (≈ 250 W), consistent with power-limiting mechanisms documented by NVIDIA (i.e., performance/power capping). Such caps introduce a saturation regime where power no longer scales linearly with workload, creating non-stationary dynamics that can degrade purely data-driven linear models. This motivates incorporating physically informed constraints (as in PI-DLinear) to improve robustness and generalization under operational limits. Furthermore, the combination of dense sampling and extended temporal coverage implies substantial non-stationarity (e.g., workload shifts, diurnal/weekly cycles, and IT maintenance activities), making the benchmark more representative of real data-center conditions than short or sparsely sampled traces. This scale also stresses model efficiency, since training and inference must operate over hundreds of thousands of time points while maintaining accuracy across different prediction horizons, which further substantiates the reason why Physics-informed DLinear (PI-DLinear) was selected, as it offers high performance and low computational complexity, making it deployable to the control and monitoring units and/or microcontrollers available at AI data centers.
3.4
Computational Burden
Table 3 highlights a clear efficiency–capacity trade-off. FiLM is the most expensive option, with 12.9M parameters, 271.38 s per epoch, and 49.30 MB memory, approximately 134× more parameters, 26× longer runtime, and 131× higher memory than DLinear. TiDE sits in the middle (1.62M params, 29.10 s, 6.21 MB), remaining substantially heavier than DLinear (about 17× more parameters and 2.8× slower). In contrast, DLinear is the lightest (96k params, 10.43 s, 0.376 MB) and more importantly, PI-DLinear preserves the same parameter count and memory footprint as DLinear (96k, 0.376 MB) while increasing runtime to 20.27 s (about 1.9× slower), indicating that the physics-aware component adds compute overhead without increasing model size because it’s only used in optimizing training and not during inference. The bubble chart in Fig. 6 indicates that PI-DLinear offers the best accuracy–efficiency trade-off among these four top models. It achieves the lowest MSE (0.213) at 20.27 s/epoch with a very small memory footprint (0.376 MB), suggesting that incorporating the physics-aware term improves fit without increasing model size. Relative to vanilla DLinear (MSE 0.2190, 10.43 s/epoch, 0.376 MB), PI-DLinear reduces the error by 0.006 MSE (≈ 3%) for this case (input-240-predict-80), at the cost of 1.94× higher compute time, consistent with added physics-related computation. In contrast, TiDE is both slower (29.10 s/epoch) and less accurate (0.2207 MSE) than PI-DLinear, and requires substantially more memory (6.21 MB), which aligns with its heavier encoder–decoder MLP design compared to linear baselines. Finally, FiLM is an extreme outlier in cost, 271.38 s/epoch and 49.30 MB, yet delivers no accuracy benefit (MSE 0.2192, essentially comparable to DLinear), making it dominated in this setting, where it consumes orders of magnitude more compute/memory without improving (decreasing) the forecasting error. 10
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
Table 3: Model complexity and inference efficiency for a single forward pass, reported in terms of parameter count, runtime (seconds), and peak memory usage (MB). Model
#Params
Time (s)
Memory (MB)
TiDE FiLM DLinear PI-DLinear
1 624 359 12 923 662 96 160 96 160
29.10 271.38 10.43 20.27
6.210 49.30 0.376 0.376
3.5
Predicting Power Throttling
3.5.1
Throttle Event Detection
Table 7 in the appendix (Section C) presents the throttle detection performance across different sequence lengths and prediction horizons. PI-DLinear consistently outperforms the baseline DLinear in detecting power throttling events, achieving improved detection rates in the configurations tested. The most substantial improvement occurs at sequence length L = 360 with prediction horizon T = 10, where PI-DLinear achieves a detection rate of 85.03% compared to 65.29% for DLinear, an improvement of 19.75%. However, at very short horizons (T = 5), DLinear actually outperforms PI-DLinear in detection rate. This suggests the physics constraints are most beneficial for longer prediction horizons (T ≥ 10), where the thermal dynamics have more time to manifest. This is further substantiated by the interesting observation, which is that PI-DLinear reaches near-perfect detection at longer horizons, achieving 99.12% detection rate at L = 480, H = 80 compared to 96.27% for DLinear. Overall, on average across all configurations, PIDLinear improves the throttle detection rate by 6.88%, demonstrating that the physics-informed constraints effectively encode the relationship between sustained high utilization and impending power reduction. 3.5.2
Throttle Event Prediction Accuracy
Beyond detection rate, we evaluate prediction accuracy specifically at throttle event timesteps using Throttle MAE and Throttle RMSE. PI-DLinear achieves an average Throttle RMSE improvement of 3.92% across all prediction lengths, with the most significant improvement of 28.61% observed at L = 360, T = 20 (RMSE reduced from 0.396 to 0.283 in normalized units, corresponding to a reduction from 1,256 W to 897 W in original units). This improvement further underscores that physics-informed thermal constraints enable the model to better anticipate the magnitude of power drops during throttling events. While Throttle MAE shows marginal average improvement (0.15%), this is expected as MAE is less sensitive to large prediction errors that occur during sudden power transitions. Yet, the combination of higher detection rates and lower RMSE indicates that PI-DLinear not only identifies more throttling
Mean Squared Error (MSE)
0.222
TiDE 29.1s, 6.21MB
0.220
DLinear 10.4s, 0.38MB
0.218
FiLM 271.4s, 49.3MB
0.216 0.214 PI-DLinear 20.3s, 0.38MB
0.212 0
50
100 150 200 Computation Time per Epoch (s)
250
300
Figure 6: Bubble chart showing model efficiency comparison under input-240-predict-80 for the top 4 models. PIDlinear has the lowest MSE error with a computational time slightly higher than baseline DLinear. GPU model used: NVIDIA GeForce RTX 4080, CUDA version: 12.9. The model size was obtained from the checkpoint MB saved on disk. 11
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
Table 4: Ablation study across the investigated forecasting horizons for multivariate power forecasting of AI data centers. We report MAPE and MSE (lower is better) for DLinear, PI-DLinear (fixed λ), and self-adaptive PI-DLinear. Horizon 5
Horizon 10
Horizon 20
Horizon 40
Horizon 80
Model
MAPE
MSE
MAPE
MSE
MAPE
MSE
MAPE
MSE
MAPE
MSE
Derived ODE Solution DLinear PI-DLinear + Constant λ Self-Adaptive PI-DLinear
0.7409 0.7331 0.7317 0.7309
0.1002 0.0994 0.0993 0.0992
0.8420 0.8422 0.8407 0.8377
0.1233 0.1236 0.1234 0.1232
0.9574 0.9606 0.9561 0.9554
0.1525 0.1531 0.1527 0.1526
1.1963 1.1951 1.1939 1.1780
0.1886 0.1897 0.1893 0.1886
1.5252 1.5250 1.5088 1.4987
0.2150 0.2172 0.2165 0.2155
Note: Bold denotes the best result per column; underline denotes the second best. The values are averaged over each look-back window.
events but also predicts their severity more accurately, validating the effectiveness of incorporating thermal physics and utilization-based constraints into the forecasting framework.
3.6
Ablation Study
Across all horizons, adding physics-aware constraints consistently improves forecasting performance relative to the stateof-the-art DLinear, with the gains becoming more noticeable as the prediction window grows, further demonstrating the potential of the proposed model for long-term power forecasting. Even with a fixed physics weight (λ = 0.005), PI-DLinear reduces both MAPE and MSE at every horizon (e.g., MAPE drops from 1.5250 to 1.5088 at prediction length of 80 min), indicating that the newly derived second-order RC constraint acts as a useful regularizer for power-thermal dynamics. Ultimately, the self-adaptive weighting variant delivers the best and most consistent improvements, achieving the best scores for every prediction length averaged over the investigated look-back windows and providing the largest long-horizon performance enhancement (e.g., MAPE 1.4987 and MSE 0.2155 at a prediction length of 80 min) as outlined in Table 4, which suggests that dynamically balancing data fit and physics residuals is important when error accumulation and regime shifts (i.e., throttling-related transients) become more prevalent at longer horizons. This is further corroborated by the large improvements observed in Fig. 1, where the physics and throttle constraints encoded into the loss function of DLinear, delivered (1) improved transient recovery forecasting performance under abrupt AI load fluctuations, (2) stable predictions even after power throttling subsides, and (3) allowed for capturing GPU power throttling events. Lastly, considering the derived ODE solution alone, which considers power and thermal behavior, inertia (time constant) and coupling effects are therefore inherently present in the data center. Therefore, over longer prediction horizons, these slower physical mechanisms become more prominent, so the proposed ODE-based reconstruction was able to produce better global trajectory forecasts, which led to an improvement in the MSE error and became more competitive with the other models in Table 4. Such results further substantiate the viability of the derived ODEs, qualifying them to be integrated as the Physics component within the proposed PI-DLinear model.
4
Conclusion
In this work, we addressed short-term AI data-center power forecasting under highly transient GPU workloads by introducing PI-DLinear, a physics-aware variant of DLinear that embeds a multi-node lumped thermal RC network consistent with Newton’s law of cooling as a differentiable loss constraint. The model links the power drawn to GPU/memory thermal dynamics, thereby improving generalization across various history/lookback windows and forecasting horizons. Moving on, regarding the MIT Supercloud trace, PI-DLinear consistently outperformed stateof-the-art transformer and non-transformer baselines across multiple look-back lengths and horizons, with the most reliable gains appearing in MSE/MAPE/RMSE, the metrics most sensitive to the inherent costly spikes in the data. More importantly, PI-DLinear preserves DLinear’s lightweight footprint, incurring overhead primarily during training due to the added physics term, which supports practical deployment in monitoring/control units present in AI data centers, where efficiency matters. Finally, the ablation study highlights that physics weighting is essential, since overly strong regularization can degrade forecasting accuracy by over-constraining the data-driven optimum, especially when considering power throttling and load transient events. 12
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
References Liuzixuan Lin and Andrew A Chien. Adapting datacenter capacity for greener datacenters and grid. In Proceedings of the 14th ACM International Conference on Future Energy Systems, e-Energy ’23, page 200–213, New York, NY, USA, 2023. Association for Computing Machinery. ISBN 9798400700323. doi:10.1145/3575813.3595197. URL https://doi.org/10.1145/3575813.3595197. Mark Haranas. Google pours billions into new u.s. data centers: Here’s where, 2024. URL https://www.crn.com/ news/cloud/2024/google-pours-billions-into-new-u-s-data-centers-here-s-where. Accessed: 2025-11-16. Dan Swinhoe. Oracle’s larry ellison: We’re building out 100 data centers globally, 2024. URL https://www.cnbc. com/2024/. Accessed: 2025-11-16. Aurora Energy Research. Data center load growth in pjm, 2024. URL https://auroraer.com/resources/ aurora-insights/market-reports/data-center-load-growth-in-pjm. Accessed: 2025-11-17. Liuzixuan Lin, Rajini Wijayawardana, Varsha Rao, Hai Nguyen, Emmanuel Wedan GNIBGA, and Andrew A. Chien. Exploding ai power use: an opportunity to rethink grid planning and management. In Proceedings of the 15th ACM International Conference on Future and Sustainable Energy Systems, e-Energy ’24, page 434–441, New York, NY, USA, 2024. Association for Computing Machinery. ISBN 9798400704802. doi:10.1145/3632775.3661959. URL https://doi.org/10.1145/3632775.3661959. Schneider Electric and NVIDIA. Ai reference designs to enable adoption: A collaboration between schneider electric and nvidia. White paper, Schneider Electric, 2023. URL https://www.se.com/ww/en/download/document/ SPD_EB1_EN/. Accessed: 2025-11-19. Y. Li, M. Mughees, Y. Chen, and Y. R. Li. The unseen ai disruptions for power grids: Llm-induced transients. arXiv preprint arXiv:2409.11416, 2024. URL https://arxiv.org/abs/2409.11416. Haixu Wu, Tengge Hu, Yong Liu, Hang Zhou, Jianmin Wang, and Mingsheng Long. Timesnet: Temporal 2d-variation modeling for general time series analysis, 2023. URL https://arxiv.org/abs/2210.02186. Siddharth Samsi, Matthew L Weiss, David Bestor, Baolin Li, Michael Jones, Albert Reuther, Daniel Edelman, William Arcand, Chansup Byun, John Holodnack, Matthew Hubbell, Jeremy Kepner, Anna Klein, Joseph McDonald, Adam Michaleas, Peter Michaleas, Lauren Milechin, Julia Mullen, Charles Yee, Benjamin Price, Andrew Prout, Antonio Rosa, Allan Vanterpool, Lindsey McEvoy, Anson Cheng, Devesh Tiwari, and Vijay Gadepally. The mit supercloud dataset, 2021. URL https://arxiv.org/abs/2108.02037. Maziar Raissi. Deep hidden physics models: deep learning of nonlinear partial differential equations. J. Mach. Learn. Res., 19(1):932–955, January 2018. ISSN 1532-4435. Levi D. McClenny and Ulisses M. Braga-Neto. Self-adaptive physics-informed neural networks. Journal of Computational Physics, 474:111722, 2023. ISSN 0021-9991. doi:https://doi.org/10.1016/j.jcp.2022.111722. URL https://www.sciencedirect.com/science/article/pii/S0021999122007859. George Amvrosiadis, Jae W. Park, Gregory R. Ganger, Garth A. Gibson, Ethan Baseman, and Nathan DeBardeleben. On the diversity of cluster workloads and its impact on research results. In 2018 USENIX Annual Technical Conference (USENIX ATC 18), pages 533–546. USENIX Association, 2018. Marcel Blöcher, Lin Wang, Patrick Eugster, and Max Schmidt. Switches for hire: resource scheduling for data center in-network computing. In Proceedings of the 26th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, ASPLOS ’21, page 268–285, New York, NY, USA, 2021. Association for Computing Machinery. ISBN 9781450383172. doi:10.1145/3445814.3446760. URL https: //doi.org/10.1145/3445814.3446760. Grant Wilkins, Srinivasan Keshav, and Richard Mortier. Hybrid heterogeneous clusters can lower the energy consumption of llm inference workloads. In Proceedings of the 15th ACM International Conference on Future and Sustainable Energy Systems, e-Energy ’24, page 506–513, New York, NY, USA, 2024. Association for Computing Machinery. ISBN 9798400704802. doi:10.1145/3632775.3662830. URL https://doi.org/10.1145/3632775.3662830. Sheng Wang, Shiping Chen, and Yumei Shi. Utilization-prediction-aware energy optimization approach for heterogeneous gpu clusters. The Journal of Supercomputing, 80:9554–9578, May 2024. doi:https://doi.org/10.1007/s11227023-05807-x. Maurizio Rossi and Davide Brunelli. Forecasting data centers power consumption with the holt-winters method. In 2015 IEEE Workshop on Environmental, Energy, and Structural Monitoring Systems (EESMS) Proceedings, pages 210–214, 2015. doi:10.1109/EESMS.2015.7175879. 13
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
David Meisner, Brian T. Gold, and Thomas F. Wenisch. Powernap: eliminating server idle power. In Proceedings of the 14th International Conference on Architectural Support for Programming Languages and Operating Systems, ASPLOS XIV, page 205–216, New York, NY, USA, 2009. Association for Computing Machinery. ISBN 9781605584065. doi:10.1145/1508244.1508269. URL https://doi.org/10.1145/1508244.1508269. Hayk Shoukourian and Dieter Kranzlmüller. Forecasting power-efficiency related key performance indicators for modern data centers using lstms. Future Generation Computer Systems, 112:362–382, 2020. ISSN 0167-739X. doi:https://doi.org/10.1016/j.future.2020.05.014. URL https://www.sciencedirect.com/science/article/ pii/S0167739X20303964. Lu Bai, Weixing Ji, Qinyuan Li, Xilai Yao, Wei Xin, and Wanyi Zhu. Dnnabacus: Toward accurate computational cost prediction for deep neural networks, 2022. URL https://arxiv.org/abs/2205.12095. Pratyush Patel, Esha Choukse, Chaojie Zhang, Íñigo Goiri, Brijesh Warrier, Nithish Mahalingam, and Ricardo Bianchini. Characterizing power management opportunities for llms in the cloud. In Proceedings of the 29th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 3, ASPLOS ’24, page 207–222, New York, NY, USA, 2024. Association for Computing Machinery. ISBN 9798400703867. doi:10.1145/3620666.3651329. URL https://doi.org/10.1145/3620666.3651329. Qinghao Hu, Peng Sun, Shengen Yan, Yonggang Wen, and Tianwei Zhang. Characterization and prediction of deep learning workloads in large-scale gpu datacenters. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC ’21, New York, NY, USA, 2021. Association for Computing Machinery. ISBN 9781450384421. doi:10.1145/3458817.3476223. URL https://doi.org/10.1145/ 3458817.3476223. Mariam Mughees, Yuzhuo Li, Yize Chen, and Yunwei Ryan Li. Short-term load forecasting for ai-data center, 2025. URL https://arxiv.org/abs/2503.07756. Tiechui Yao, Jue Wang, Yangang Wang, Pei Zhang, Haizhou Cao, Xuebin Chi, and Min Shi. Very short-term forecasting of distributed pv power using gstann. CSEE Journal of Power and Energy Systems, 10(4):1491–1501, 2024. doi:10.17775/CSEEJPES.2022.00110. Muhammad Aslam, Seung-Jae Lee, Sang-Hee Khang, and Sugwon Hong. Two-stage attention over lstm with bayesian optimization for day-ahead solar power forecasting. IEEE Access, 9:107387–107398, 2021. doi:10.1109/ACCESS.2021.3100105. Mohammad Safayet Hossain and Hisham Mahmood. Short-term photovoltaic power forecasting using an lstm neural network and synthetic weather forecast. IEEE Access, 8:172524–172533, 2020. doi:10.1109/ACCESS.2020.3024901. Jianjing Li, Chenghui Zhang, and Bo Sun. Two-stage hybrid deep learning with strong adaptability for detailed day-ahead photovoltaic power forecasting. IEEE Transactions on Sustainable Energy, 14(1):193–205, 2023. doi:10.1109/TSTE.2022.3206240. Qingsong Wen, Tian Zhou, Chaoli Zhang, Weiqi Chen, Ziqing Ma, Junchi Yan, and Liang Sun. Transformers in time series: a survey. In Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, IJCAI ’23, 2023. ISBN 978-1-956792-03-4. doi:10.24963/ijcai.2023/759. URL https://doi.org/10.24963/ijcai. 2023/759. Shiyang Li, Xiaoyong Jin, Yao Xuan, Xiyou Zhou, Wenhu Chen, Yu-Xiang Wang, and Xifeng Yan. Enhancing the locality and breaking the memory bottleneck of transformer on time series forecasting. Curran Associates Inc., Red Hook, NY, USA, 2019. Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. Informer: Beyond efficient transformer for long sequence time-series forecasting. In Proceedings of the AAAI conference on artificial intelligence, volume 35, pages 11106–11115, 2021. Haixu Wu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. Autoformer: decomposition transformers with autocorrelation for long-term series forecasting. In Proceedings of the 35th International Conference on Neural Information Processing Systems, NIPS ’21, Red Hook, NY, USA, 2021. Curran Associates Inc. ISBN 9781713845393. Shizhan Liu, Hang Yu, Cong Liao, Jianguo Li, Weiyao Lin, Alex X. Liu, and Schahram Dustdar. Pyraformer: Lowcomplexity pyramidal attention for long-range time series modeling and forecasting. In International Conference on Learning Representations, 2022. URL https://openreview.net/forum?id=0EXmFzUn5I. Razvan-Gabriel Cirstea, Chenjuan Guo, Bin Yang, Tung Kieu, Xuanyi Dong, and Shirui Pan. Triformer: Triangular, variable-specific attentions for long sequence multivariate time series forecasting–full version, 2022. URL https: //arxiv.org/abs/2204.13767. 14
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
Tian Zhou, Ziqing Ma, Qingsong Wen, Xue Wang, Liang Sun, and Rong Jin. Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting. In International conference on machine learning, pages 27268–27286. PMLR, 2022. Ailing Zeng, Muxi Chen, Lei Zhang, and Qiang Xu. Are transformers effective for time series forecasting? In Proceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence, AAAI’23/IAAI’23/EAAI’23. AAAI Press, 2023. ISBN 978-1-57735-880-0. doi:10.1609/aaai.v37i9.26317. URL https://doi.org/10.1609/aaai.v37i9.26317. Ulisses Braga-Neto. Physics-informed machine learning. In Fundamentals of Pattern Recognition and Machine Learning, pages 293–324. Springer, 2024. NVIDIA Corporation. Tesla V100 PCIe GPU Accelerator: Product Brief. NVIDIA Corporation, March 2018. URL https://images.nvidia.com/content/tesla/pdf/Tesla-V100-PCIe-Product-Brief.pdf. Document ID: PB-08744-001_v05. Ulisses Braga-Neto. Fundamentals of pattern recognition and machine learning. Springer, 2020. Seongho Bak, Sowon Choi, Donguk Yang, Doyoon Kim, Heeseon Rho, and Kyoobin Lee. Transfer learning for photovoltaic power forecasting across regions using large-scale datasets. IEEE Access, 13:136175–136190, 2025. doi:10.1109/ACCESS.2025.3591040. Hai-Peng Deng, Yan-Bo He, Bing-Chuan Wang, and Han-Xiong Li. Physics-dominated neural network for spatiotemporal modeling of battery thermal process. IEEE Transactions on Industrial Informatics, 20(1):452–460, 2023.
A
Physics-Informed Neural Networks
During forward modelling, the initial and boundary conditions are assumed to be known, bringing us to the common ODE solving problem, where PINN is leveraged as a conventional numerical solver approach. With that, let the unknown u(x, t) be determined by an ansatz u(x, t; w), comprising a NN with input features x = (x1 , ..., xd ), time t to study the temporal correlations, and network weights w. Merely one output is approximated (regression problem) as u is a scalar function. However, given a ODE/PDE system, multiple outputs can be acquired, one for each variable. To this end, the objective is to obtain network weights w such that McClenny and Braga-Neto [2023] F (u(x, t; w), x, t, Du(x, t; w), D2 u(x, t; w), ..., Dk u(x, t; w); λ) = f (x, t).
x, t ∈ Ω
(15)
The partial derivatives Dα u(x; w) of the NN output, for x and w at time t in function F , is calculated using automatic differentiation methods. Therefore, it is worth noting the loss functions as McClenny and Braga-Neto [2023] Z 2 Lu (w) = |û(x, t) − u(x, t)| dx, Ω Z (16) Lr (w, λ) = F u(x, t; w), x, t, Du(x, t; w), Ω 2 D2 u(x, t; w), . . . , Dk u(x, t; w); λ − f (x, t) dx.
Lu is the mean-squared error (MSEu ) that the NN incorporates to forecast the initial and boundary conditions, as well Nu as utilizing training data for calibration represented via xiu , tiu , ui i=1 , with û defined as the predicted label based i i i on the input xu at time tu and compared with the true label u . Lr is the MSEr , which consists of evaluations of the Nr residual/physics function f over xir , tir i=1 with input xir at time tif Deng et al. [2023]. Conventionally, the integrals in Equation (16) is numerically approximated by constructing Monte-Carlo estimates through uniformly distributed i i Nu r random samples {xir , tir }N i=1 ⊂ Ω and {xu , tu }i=1 ⊂ Ω as McClenny and Braga-Neto [2023] Nu . 1 X Lu (w) = û(xiu , tiu ) − u(xiu , tiu ) , Nu i=1 N
r . 1 X F u(xir , tir ; w), xir , tir , Du(xir , tir ; w), Lr (w) = Nr i=1
2 D2 u(xir , tir ; w), . . . , Dm u(xir , tir ; w); λ − f (xir , tir ) .
15
(17)
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
B
Methodology
B.1
Problem Statement
A PREPRINT
We address the problem of short-term power forecasting for GPU-accelerated data centers. Given a multivariate time series of GPU telemetry X = {x1 , x2 , . . . , xL } ∈ RL×C , (18) where L is the historical lookback window and each observation xt ∈ RD comprises C = 5 features/co-variates h i⊤ (m) (g) (m) xt = u(g) , (19) u T T P t t t t t representing GPU utilization (u(g) ), memory utilization (u(m) ), GPU temperature (T (g) ), memory temperature (T (m) ), and electrical power consumption (P ), respectively. Our objective is to predict future power consumption over a horizon T as ŷ = {P̂L+1 , P̂L+2 , . . . , P̂L+T } ∈ RT . B.2
(20)
Thermal-Electrical Analogy: Theoretical Foundation
The foundation of our physics-informed approach lies in the well-established thermal-electrical analogy, which maps heat transfer phenomena to equivalent electrical circuits. This analogy arises from the mathematical similarity between Fourier’s law of heat conduction and Ohm’s law of electrical conduction. B.2.1
Fundamental Analogies
The thermal-electrical analogy establishes the following correspondences. Table 5: Thermal-Electrical Analogy Quantity Potential (Across variable) Flow (Through variable) Resistance Capacitance Source
B.2.2
Thermal Domain
Electrical Domain
Temperature T [K] Heat flow Q̇ [W] Thermal resistance Rth [K/W] Thermal capacitance Cth [J/K] Heat source P [W]
Voltage V [V] Current I [A] Electrical resistance R [Ω] Electrical capacitance C [F] Current source I [A]
Governing Equations
Ohm’s Law (Electrical): V R
(21)
∆T Rth
(22)
V =I ·R
⇐⇒
I=
∆T = Q̇ · Rth
⇐⇒
Q̇ =
Fourier’s Law (Thermal):
Capacitor Equation (Electrical): I=C
dV dt
(23)
dT dt
(24)
Thermal Mass Equation: Q̇ = Cth
where the thermal capacitance Cth = m · cp is the product of mass m and specific heat capacity cp . 16
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
B.3
A PREPRINT
Lumped-Parameter Thermal Model for GPU Systems
Modern GPUs consist of multiple thermally-coupled components. We employ a lumped-parameter approach, which assumes spatial temperature uniformity within each component. This assumption is well-justified for GPU and memory modules given their high thermal conductivity and small dimensions. B.3.1
Two-Node RC Thermal Network
We model the GPU system as a coupled two-node thermal network comprising: • Node 1 (GPU): Temperature Tg , thermal capacitance Cg • Node 2 (Memory): Temperature Tm , thermal capacitance Cm • Reference (Ambient): Temperature Ta (assumed constant or slowly varying) The thermal resistances are: • Rga : GPU to ambient (through heatsink/airflow) • Rma : Memory to ambient • Rgm : GPU to memory (thermal coupling through PCB/substrate) B.4
Equivalent Circuit Derivation Ta
Rma
Ambient
Tm −Ta Rma
Rgm
Tm Cm
Tg −Tm Rgm
Tg
αP (1−α)P
Cg
Memory GPU Thermal-Electrical Analogy: Temperature T ↔ Voltage V Heat flow Q̇ ↔ Current I Thermal resistance Rth ↔ Resistance R Thermal capacitance Cth ↔ Capacitance C Heat source P ↔ Current source I
Governing ODEs (Kirchhoff’s Current Law at each node): Tg − Ta dTg Tg − Tm = αP − − dt Rga Rgm
GPU Node (Tg ) :
Cg
Memory Node (Tm ) :
Cm
dTm Tm − Ta Tg − Tm = (1 − α)P − + dt Rma Rgm
Figure 7: Equivalent RC thermal circuit for coupled GPU-Memory system. Current sources represent heat input from electrical power dissipation (P split by factor α). Capacitors represent thermal mass (ability to store thermal energy). Resistors represent thermal resistance to heat flow. Applying Kirchhoff’s Current Law at each node yields the governing ODEs. B.5
Derivation of Governing ODEs via Kirchhoff’s Current Law
Applying Kirchhoff’s Current Law (KCL) at each node, stating that the sum of currents entering a node equals the sum of currents leaving, we derive the governing ordinary differential equations. B.5.1
Node 1: GPU Die (Tg )
At the GPU node, the heat balance is: (g)
(g)
Heat input
Heat stored
Q̇in = Q̇stored + |{z} | {z }
Q̇ga |{z}
Heat to ambient
17
+
Q̇gm |{z}
Heat to memory
(25)
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
Substituting the constitutive relations: Tg − Ta Tg − Tm dTg + + dt Rga Rgm
(26)
dTg Tg − Ta Tg − Tm = αP − − dt Rga Rgm
(27)
αP = Cg Rearranging to standard ODE form: Cg B.5.2
Node 2: Memory (Tm )
Similarly, at the memory node: (m)
Q̇in + | {z }
Heat input
Q̇gm |{z}
(m)
Heat from GPU
= Q̇stored + | {z } Heat stored
Q̇ma |{z}
(28)
Heat to ambient
Note that heat flows into the memory node from the GPU when Tg > Tm : Tm − Ta Tg − Tm dTm + = Cm Rgm dt Rma
(29)
dTm Tm − Ta Tg − Tm = (1 − α)P − + dt Rma Rgm
(30)
(1 − α)P + Rearranging: Cm
Table 6: Physical interpretation of RC thermal network parameters
B.6
Symbol
Name
Units
Physical Meaning
Cg Cm Rga Rma Rgm Ta α
GPU thermal capacitance Memory thermal capacitance GPU-to-ambient resistance Memory-to-ambient resistance GPU-memory coupling resistance Ambient temperature Power split factor
J/K J/K K/W K/W K/W K –
Heat required to raise GPU temp by 1K Heat required to raise memory temp by 1K Temp rise per watt dissipated to ambient Temp rise per watt dissipated to ambient Thermal coupling strength between components Reference/environment temperature Fraction of total power dissipated in GPU
Power-Temperature Rate Relationship
A key insight for power forecasting is that Equations (27) and (30) can be inverted to express power in terms of temperature dynamics. From the GPU thermal ODE, we get Cg
dTg Tg − Ta Tg − Tm = αP − − . dt Rga Rgm
(31)
P =
1 dTg Tg − Ta Tg − Tm Cg + + α dt Rga Rgm
(32)
Solving for P :
Differentiating both sides with respect to time yields the power rate constraint as dP 1 d2 Tg 1 dTg 1 dTg dTm = Cg 2 + + − dt α dt Rga dt Rgm dt dt
(33)
Combining terms: dP 1 d2 Tg 1 1 dTg 1 dTm = Cg 2 + + − dt α dt Rga Rgm dt Rgm dt 18
(34)
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
Table 7: Throttle Detection Performance. Comparison of DLinear (baseline) and PI-DLinear across different sequence lengths (L) and prediction horizons (T ). Detection Rate measures the percentage of true throttle events identified. Throttle MAE and RMSE measure prediction accuracy specifically at throttle event timesteps. Bold indicates better performance. ∆ columns show improvement of PI-DLinear over DLinear. L
T
Detection Rate (%) DLinear PI-DLinear ∆ (pp)
DLinear
240 240 240 240 240
5 10 20 40 80
61.92 65.45 62.92 63.85 68.70
44.35 71.52 76.47 74.41 87.54
-17.57 +6.06 +13.55 +10.56 +18.85
0.1106 0.1455 0.1638 0.2051 0.2290
0.1221 0.1398 0.1635 0.2058 0.2358
-10.39 +3.92 +0.17 -0.36 -2.96
0.1721 0.3177 0.3790 0.4993 0.5279
0.2734 0.2925 0.3725 0.5187 0.5233
-58.85 +7.94 +1.70 -3.89 +0.88
360 360 360 360 360
5 10 20 40 80
68.95 65.29 72.00 75.00 85.37
66.53 85.03 86.93 85.85 86.68
-2.42 +19.75 +14.93 +10.85 +1.31
0.1324 0.1431 0.1627 0.2001 0.2364
0.1384 0.1565 0.1578 0.2001 0.2380
-4.53 -9.38 +2.99 -0.01 -0.67
0.3821 0.3645 0.3962 0.4644 0.5215
0.3989 0.3973 0.2828 0.4575 0.5251
-4.40 -9.01 +28.61 +1.49 -0.68
480 480 480 480 480
5 10 20 40 80
71.10 81.95 83.81 88.26 96.27
66.92 78.40 85.90 95.54 99.12
-4.18 -3.55 +2.09 +7.28 +2.85
0.1562 0.1646 0.1782 0.2098 0.2557
0.1759 0.1727 0.1731 0.2081 0.2563
-12.60 -4.96 +2.90 +0.77 -0.23
0.5264 0.4391 0.4322 0.5072 0.5513
0.6239 0.4355 0.4066 0.4581 0.5498
-18.53 +0.83 +5.93 +9.67 +0.28
600 600 600 600 600
5 10 20 40 80
80.24 83.08 83.16 89.29 90.75
71.37 86.40 90.31 91.90 95.15
-8.87 +3.32 +7.14 +2.62 +4.41
0.1627 0.1691 0.1721 0.2086 0.2559
0.1656 0.1670 0.1784 0.1952 0.2480
-1.75 +1.22 -3.63 +6.41 +3.12
0.5413 0.4068 0.4105 0.4538 0.5002
0.4586 0.3825 0.3996 0.4246 0.4960
+15.27 +5.97 +2.67 +6.43 +0.83
C
Throttle MAE PI-DLinear ∆ (%)
Throttle RMSE DLinear PI-DLinear ∆ (%)
Power Throttling Prediction Results
The power throttling predictions results are summarized in Tables 7 and 8.
D
Weight Visualization of PI-Dlinear
Fig. 8 presents the heatmaps of the trend and seasional components of the proposed PI-DLinear model. The heatmaps can be interpreted as time-varying linear attribution maps, where for each forecast step t ∈ {1, ..., T } (y-axis), PIDLinear assigns a weight to each look-back/sequence length index k ∈ {0, ..., L − 1} (x-axis), and the prediction is formed by a weighted aggregation of the decomposed history. This interpretation is consistent with the DLinear family, which performs a moving-average decomposition into trend and remainder/seasonal components and then applies separate linear projections whose outputs are summed to produce the final forecast. The seasonal heatmap shows higher spatial variability across the look-back window and more pronounced sign changes (positive vs. negative weights), consistent with a remainder branch that corrects for higher-frequency, short-term deviations rather than extrapolating a smooth trajectory. Moreover, most early-to-mid history indices contribute with relatively small magnitude (near-zero/teal color), while the model places structured emphasis on a recent sub-window, i.e. a region of positive weights (yellow-green) appears in the later part of the look-back window, followed by a strong negative band (dark purple) closer to the end of the window, and then a narrow return to positive at the extreme right edge. Functionally, this indicates a contrastive use of recent lags, boosting certain recent oscillations while suppressing others, to shape the seasonal correction, underscoring the importance of adding a physics-based regularizer/constraint to the loss function as means to improve model apprehensibility across the entire horizon of such highly variable data. Across the forecast steps, these patterns are broadly similar but not identical, suggesting the seasonal head learns horizon-dependent adjustments (i.e., the correction for step t = 1 is not identical to that for step t = T ), which is exactly where a seasonal/residual branch is expected to express step-specific behavior. The trend heatmap is smoother and more coherent across the look-back axis, with substantially less fine-grained alternation than the seasonal map. The most salient feature is the strong concentration of positive weights at the far-right edge (largest look-back indices, i.e., the most recent observations), indicating that the trend forecast is dominated by the 19
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
(a) Trend component. Weight map for the trend branch, exhibiting smoother structure and stronger emphasis on recent history, consistent with a stable baseline extrapolation across horizons.
(b) Seasonal (remainder) component. Weight map for the seasonal branch, showing structured, sign-varying lag contributions that provide horizon-dependent residual corrections.
Figure 8: Learned linear projection weights of PI-DLinear over the look-back window for each forecast step. The x-axis denotes the look-back index (0, ..., L − 1) up to L = 240 min, the y-axis denotes the forecast step (0, ..., T ) up to T = 5 min, and the colors encode the signed weight magnitude, indicating whether each lag contributes positively or negatively to the forecast.
20
A Physics-Aware Framework for Short-Term Power Forecasting of AI Data Centers
A PREPRINT
Table 8: Throttle Detection Performance. Detection Rate (%), Throttle MAE, and Throttle RMSE for DLinear (DL) and PI-DLinear (PI). Bold indicates better performance.
L
T
Det. Rate (%) DL PI
Thr. MAE DL PI
Thr. RMSE DL PI
240 240 240 240 240
5 10 20 40 80
61.9 65.5 62.9 63.9 68.7
44.4 71.5 76.5 74.4 87.5
0.111 0.146 0.164 0.205 0.229
0.122 0.140 0.164 0.206 0.236
0.172 0.318 0.379 0.499 0.528
0.273 0.293 0.373 0.519 0.523
360 360 360 360 360
5 10 20 40 80
69.0 65.3 72.0 75.0 85.4
66.5 85.0 86.9 85.9 86.7
0.132 0.143 0.163 0.200 0.236
0.138 0.157 0.158 0.200 0.238
0.382 0.365 0.396 0.464 0.522
0.399 0.397 0.283 0.458 0.525
480 480 480 480 480
5 10 20 40 80
71.1 82.0 83.8 88.3 96.3
66.9 78.4 85.9 95.5 99.1
0.156 0.165 0.178 0.210 0.256
0.176 0.173 0.173 0.208 0.256
0.526 0.439 0.432 0.507 0.551
0.624 0.436 0.407 0.458 0.550
600 600 600 600 600
5 10 20 40 80
80.2 83.1 83.2 89.3 90.7
71.4 86.4 90.3 91.9 95.2
0.163 0.169 0.172 0.209 0.256
0.166 0.167 0.178 0.195 0.248
0.541 0.407 0.411 0.454 0.500
0.459 0.383 0.400 0.425 0.496
latest level/slope information. Earlier history contributes comparatively weakly and more uniformly, consistent with a trend estimator that prioritizes the recent trends of the data. Moreover, the weight pattern is also more stable across the forecast steps, implying that the trend head implements a relatively consistent extrapolation mechanism for all horizons, while the seasonal head accounts for more horizon-specific corrections. This can be further attributed to the fact that the intermittent nature of the data during training the model to focus on the more recent look-back index and gradually decrease the attention to the earlier historical time steps to ultimately make the error residual in the loss function for the physics and data components as close as possible to/near ≈ 0. For a given forecast step t, PI-DLinear forms the prediction as a weighted sum over the look-back window as ŷt =
L−1 X
wt,k xk ,
(35)
k=0
where we ignore the bias term and the final summation over the components for simplicity. If wt,k > 0, then xk yields a positive contribution to ŷt . Holding everything else fixed, a change ∆xk induces a change in the forecast of approximately wt,k ∆xk . If wt,k < 0, then xk yields a negative contribution to ŷt . Holding everything else fixed, a change ∆xk induces a change in the forecast of approximately wt,k ∆xk (negative when ∆xk > 0). This provides a local linear interpretation of the heatmap, where each cell indicates how strongly and with what sign a specific look-back index contributes to the prediction at a given horizon.
21