Demographically-Informed Heat-Mortality Risk Curves via Risk Graph Neural Networks Alex O. Davies1 (
), Eunice Lo1 , and Rui Zhu1
arXiv:2607.21131v1 [cs.LG] 23 Jul 2026
School of Geographical Sciences, University of Bristol, UK [email protected]
Abstract. Estimating heat-related mortality risk is a core task in environmental epidemiology, typically addressed with Distributed Lag Nonlinear Models (DLNMs); interpretable exposure-response surfaces fitted to temperature-mortality time series. DLNMs are effective but ignore demographic and geographic context, despite well-established relevance to heat vulnerability. We propose Risk Graph Neural Networks (RGNNs), a hierarchical GNN encoder that uses granular census features to optimise DLNM coefficient vectors, preserving interpretable risk curve outputs while substantially improving predictive calibration. Evaluated across 10 regions of England and Wales on two unprecedented heat years, RGNN variants maintain both lower point-errors and near-nominal uncertainty coverage during the 2022 heatwave where baselines collapse. Keywords: temperature–mortality modelling · graph neural networks · distributed lag non-linear models · spatial epidemiology
1
Introduction
A central task in environmental epidemiology is estimating mortality risk from temperature exposure. The dominant tool is the Distributed Lag Non-linear Model (DLNM) [4], which produces an interpretable exposure-response surface over a lag dimension. This captures, for instance, that cold mortality peaks 7–14 days after exposure while heat mortality concentrates in the immediate 3-day window. DLNMs operate purely on temporal signals, however, making no use of demographic or geographic features despite their established importance in mediating heat vulnerability. Recent ML approaches [1] sometimes improve point estimates but rarely match the interpretability of the DLNM risk curve, and Boudreault et al. [2] note that the DLNM is rarely used as a proper benchmark. A core reason for the wide adoption of DLNMs over other predictive models is the interpretability of their outputs. A risk curve is immediately transparent to technical and non-technical users, making it a powerful tool in informing policy decisions. We introduce Risk Graph Neural Networks (RGNNs), which augment DLNMs with a hierarchical GNN encoder over census features. The result preserves the interpretable risk curve while substantially improving calibration under distributional shift — precisely the regime that matters most for public
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health decision-making during extreme heat events. Early counterfactual experiments produce spatially-resolved, policy-relevant mortality predictions across urban areas.
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Background
Fig. 1. Risk surfaces, in units of deaths per 100k, for London. Left: Vanilla DLNM. Right: RGNN-Calibrated.
Here we briefly summarise the current state of modelling the heat-mortality relationship. DLNMs are proposed and formalised in-detail in Gasparrini et al. [4], and Boudreault et al. [2] review ML approaches. 2.1
Distributed Lag Non-linear Models (DLNMs)
A DLNM [4] models a scalar health outcome at location i and time t as a linear combination of a cross-basis matrix that encodes the joint non-linear and lagged relationship between an exposure and the outcome: ŷit = wi · CBit , ncb
(1)
where wi ∈ R is a coefficient vector estimated by ordinary least squares and CBit ∈ Rncb is the cross-basis row for location i at time t. The primary output is a exposure-outcome effect surface along lag and the exposure variable, which in our case is lag-temperature-risk, as visualised in Figure 1. Fitting one DLNM per location independently produces unstable estimates for small areas with sparse death counts, and provides no mechanism for borrowing strength from neighbouring or demographically similar locations.
Heat-Mortality Risk with GNNs
2.2
3
Graph Neural Networks (GNNs)
Graph Neural Networks [9] generalise neural networks to graph-structured data by iteratively aggregating information from local neighbourhoods. GATv2 [13] extends graph attention networks with a more expressive attention mechanism in which both source and target node features jointly determine attention weights, making it well-suited to heterogeneous hierarchies where child nodes vary substantially in informativeness. GraphSAGE [6] performs mean aggregation over sampled neighbourhoods and is widely used for spatial smoothing on geographic graphs. GNNs have been applied to urban analytics tasks including traffic forecasting [8] and air quality prediction [3], but their application to epidemiological exposure-response estimation is, to our knowledge, novel.
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Risk Graph Neural Networks (RGNNs)
The RGNN replaces per-location independent OLS with a learned mapping from census features to DLNM coefficient vectors, structured as a two-level hierarchy: a frozen per-region OLS baseline is modulated by GNN-derived corrections at both the region and LAD levels. The output preserves both the interpretability and strong prior of the OLS-initialised DLNM, while improving performance with spatially-shared demographic information, as well as being comparably cheap to run compared to full ML models. An overview of the architecture is given in Figure 2.
Fig. 2. RGNN architecture. Census features at the lowest administrative level are projected to a hidden embedding and propagated upward and laterally in separate stages, with heads predict modifying weights (Eqn. 2) over an OLS-initialised DLNM.
Initialisation. Before GNN training, per-region OLS coefficients br are estimated on region-level Pearson mortality residuals and frozen. All GNN heads are zeroinitialised, so at the start of training every LAD’s coefficient vector equals its region OLS baseline.
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Encoder. A bottom-up heterogeneous GNN propagates static demographic features from the finest available administrative unit upward through the hierarchy. At each level, child embeddings are aggregated into parent nodes using multi-head GATv2Conv attention; geographic neighbours at the same level are smoothed using SAGEConv mean aggregation. Higher-level nodes receive no direct demographic features; their representations are built entirely from upward message passing, forcing the model to learn meaningful aggregations. Coefficient prediction. Zero-initialised linear heads at each predictive level map GNN embeddings to corrections in Rncb : wi = br(i) + clamp br(i) ⊙ fls (hi ) + flsh (hi ), ±δ , (2) where ⊙ is element-wise multiplication, δ is a hyperparameter controlling the maximum correction magnitude, and the scale and shift heads modulate the shape and location of the baseline curve respectively. Importantly, weights at each level anchor independently to the same frozen baseline rather than being chained, keeping granularities independently interpretable and preventing cascading errors. With dropout, and repeat predictions of coefficients, we can form useful uncertainties that can be propagated into the vanilla DLNMs uncertainty estimations. Training objective. The primary loss is Lin’s CCC [10], which jointly penalises errors in correlation, variance ratio, and mean bias, summed at LAD and region levels with population weighting. Three auxiliary terms are added: (i) a monotonicity penalty encouraging physiologically plausible cold and heat tails; (ii) a consistency penalty penalising divergence between population-weighted LAD aggregates and region-level predictions; and (iii) a population-inverse-weighted L2 delta penalty pulling data-sparse LADs toward their regional baseline. MCdropout over the coefficient heads propagates uncertainty into the final risk curves.
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Experiments
We collect daily temperature data from HadUK [7] and LAD-level daily mortality through a data-sharing agreement with the UK ONS (2000–2024). For demographic features we use OA-level census information from Goodwin and Singleton [5] for 2021, with the implicit assumption that demographic drift is minimal across the study period. [Adjacent_To] edges connect areas sharing a boundary, e.g. (Wales) ↔ (South West); [Contains] edges encode the administrative hierarchy, e.g. (Wales) → (Cardiff). We demonstrate three RGNN variants, which share the same codebase and architecture, differing only in the depth of the administrative hierarchy: rgnn (LAD→Region, 2 levels) rgnn_lsoa (LSOA→LAD→Region, 3 levels) rgnn_oa (OA→LSOA→LAD→Region, 4 levels) As baselines we use the DLNM, Random
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Table 1. Region-level holdout evaluation across 10 regions of England and Wales. Values are mean ± standard deviation across regions. Bold indicates the best result in each column. Year Model
RMSE ↓
DLNM RF GBM LSTM† 2018 MLP†
0.33 ± 0.07 0.29 ± 0.06 0.28 ± 0.06 0.27 ± 0.04 0.29 ± 0.05
MAE ↓
Pearson ↑
CRPS ↓
Cov@90% ↑
0.25 ± 0.05 0.32 ± 0.05 0.19 ± 0.04 0.73 ± 0.03 0.22 ± 0.04 0.45 ± 0.04 0.19 ± 0.04 0.36 ± 0.02 0.21 ± 0.04 0.37 ± 0.06 0.16 ± 0.03 0.78 ± 0.03 0.21 ± 0.03 0.55 ± 0.10 — — 0.23 ± 0.04 0.48 ± 0.07 — —
RGNN 0.24 ± 0.04 0.19 ± 0.03 0.52 ± 0.08 0.14 ± 0.02 0.97 ± 0.02 RGNN-LSOA 0.24 ± 0.05 0.19 ± 0.04 0.56 ± 0.05 0.14 ± 0.02 0.99 ± 0.01 RGNN-OA 0.23 ± 0.04 0.19 ± 0.03 0.56 ± 0.05 0.14 ± 0.02 0.98 ± 0.01 DLNM RF GBM LSTM† 2022 MLP†
0.54 ± 0.09 0.52 ± 0.08 0.52 ± 0.08 0.53 ± 0.07 0.53 ± 0.08
0.44 ± 0.07 0.49 ± 0.11 0.36 ± 0.05 0.43 ± 0.06 0.43 ± 0.06 0.46 ± 0.07 0.40 ± 0.06 0.11 ± 0.03 0.43 ± 0.06 0.40 ± 0.08 0.35 ± 0.05 0.39 ± 0.07 0.46 ± 0.06 0.40 ± 0.13 — — 0.46 ± 0.07 0.48 ± 0.11 — —
RGNN 0.39 ± 0.04 0.31 ± 0.03 0.47 ± 0.07 0.22 ± 0.02 0.87 ± 0.03 RGNN-LSOA 0.39 ± 0.03 0.32 ± 0.02 0.40 ± 0.07 0.22 ± 0.02 0.89 ± 0.03 RGNN-OA 0.43 ± 0.04 0.36 ± 0.03 0.40 ± 0.07 0.25 ± 0.02 0.83 ± 0.04
Forests (RF), Gradient Boosted Models (GBM), Long Short-Term Memory networks (LSTMs) and Multi-Layer Perceptrons (MLP). RFs report their own uncertainty estimates through their ensemble, and for GBMs we use heteroscedastic noise on training residuals (std(y − ŷ)). We take two holdout sets in 2018 and 2022, both unprecedented years for heat exposure in the UK. We detrend for long-term trend, seasonality, day-ofweek effects, and public holidays using linear and Fourier terms. The outcome yit is a Pearson mortality residual; these are considered our ‘excess deaths’ not covered by these simple detrending terms, including heat-related mortality. We then normalise units to excess deaths per 100k population. For each holdout year and model we report RMSE, MAE and Pearson-correlation, as well as CRPS and Coverage@90% where uncertainty is available. Hyper-parameters for each model are optimised through a Bayesian search over RMSE with 2017 as validation year, though as is standard practise in environmental epidemiology we use the DLNM parameters from Lo et al. [11], a government-cited study on heat risk in the UK. All three RGNN variants substantially outperform DLNM on RMSE in both holdout years. In the Supplementary we provide per-region results and example risk curves from the vanilla DLNM alongside the optimised curves from our RGNNs. The most striking result is the behaviour of predictive coverage under distributional shift. In the moderate 2018 holdout, all models with uncertainty estimates achieve reasonable coverage. In 2022, however, the DLNM’s coverage
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Fig. 3. RMSE (↓), CRPS (↓), Correlation (↑) and Coverage@90% for the holdout years 2018 (top) and 2022 (bottom).
collapses to well below the nominal 90% level—while the RGNN variants maintain coverage between 0.83 and 0.89. For a public health tool intended to support decision-making during extreme heat events, calibration under tail conditions is arguably more consequential than average-year point accuracy. 4.1
Counterfactuals
As an early set of results, we vary census features at OA and examine the changes in predictions made using the RGNN-OA. We perform two experiments here; increasing the proportion of OA population with low educational qualifications (level 1/2), as well as the proportion of young adults (25-29), by one standard deviation upwards. We perform this analysis for the London region using temperature data for the 21st July 2022, the hottest day on-record in the UK. Chloropleth visualisation in Figure 4 shows heterogeneity across spatial areas, and a sweep over delta magnitudes in Figure 5 (Appendix) shows the expected relationships. Increased proportions of population with low educational levels increases mortality, and increased proportions of young people decrease it, inline with epidemiological literature on deprivation and clinical risks [12]. The North East in-general shows greater sensitivity to demographic changes, particularly in education levels, possibly due to the broadly lower socio-economic status of the region in-comparison to reason. This spatially-resolved attribution, mapping demographic vulnerability onto urban geography, exemplifies the kind of actionable, area-level intelligence that can directly inform local heat-health interventions. Further analysis will follow in future iterations of this work. 4.2
Discussion
The most consequential result is calibration: where DLNM and RF coverage collapse during the 2022 heatwave, all RGNN variants maintain near-nominal
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Fig. 4. ∆ mortality with varying census features for the RGNN-OA model on the 21st July 2022 in the London and North East regions.
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Fig. 5. ∆ predictions with varying proportions of young and lower-educated people in OAs, as predicted by the RGNN-OA in London.
coverage. For a public health tool intended to support decision-making during the events where it is needed most, this robustness under distributional shift is a meaningful contribution. Early counterfactual experiments provide evidence that the model is learning epidemiologically coherent structure rather than spurious correlations, with deprivation and age effects in the expected directions. More systematic feature attribution analysis will follow in future iterations. A natural extension is to assess whether the learned demographic embeddings transfer across geographic contexts, enabling risk curve estimation for areas with limited mortality data.
5
Conclusion
We introduced Risk Graph Neural Networks, which augment classical DLNMs with a hierarchical GNN encoder over census features, preserving interpretable risk curve outputs while substantially improving predictive calibration under extreme heat. Evaluated across 10 regions of England and Wales, RGNN variants maintain near-nominal uncertainty coverage where standard baselines collapse. Future work will broaden the geographic scope, investigate adaptive hierarchy depth, and provide fuller feature attribution analysis. We also intend to explore whether representations learned over England and Wales generalise to other health outcome data. Acknowledgments. Disclosure of Interests. The authors have no competing interests to declare that are relevant to the content of this article.
Bibliography
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A
Appendix Table 2: Per-region holdout results for all models across both holdout years. RMSE↓, MAE↓, Pearson r ↑, CRPS↓, and Coverage-90 are shown for each region under the 2018 (moderate) and 2022 (severe heatwave) holdout years. Bold indicates the best result per metric in each region-year block. For Coverage-90, best is defined as closest to the nominal 0.90 level. The Poisson noise floor (fl ) and Pearson ceiling (cl ) are shown for reference alongside each region header. † CRPS and Coverage-90 are not reported for LSTM and MLP, as these models do not produce well-defined predictive distributions.
Region Model
RMSE↓ MAE↓ Pearson↑ CRPS↓
Cov-90
North East — 2018 fl = 0.327, cl = 0.630 DLNM 0.455 0.346 0.204 0.265 RF 0.384 0.286 0.405 0.251 GBM 0.360 0.272 0.286 0.203 LSTM† 0.372 0.296 0.540 — MLP† 0.413 0.332 0.429 — RGNN 0.409 0.341 0.266 0.236 RGNNL 0.378 0.306 0.432 0.220
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Region Model
RMSE↓ MAE↓ Pearson↑ CRPS↓
RGNNOA 0.366
0.298
0.426
Cov-90
0.212
0.970
North East — 2022 fl = 0.326, cl = 0.631 DLNM 0.653 0.521 0.161 0.420 RF 0.594 0.482 0.287 0.445 GBM 0.594 0.482 0.221 0.382 LSTM† 0.527 0.449 0.240 — MLP† 0.654 0.534 0.179 — RGNN 0.362 0.260 0.255 0.202 RGNNL 0.393 0.306 0.213 0.223 RGNNOA 0.379 0.285 0.247 0.211
0.504 0.148 0.506 — — 0.964 0.975 0.964
North West — 2018 fl = 0.188, cl = 0.798 DLNM 0.321 0.245 0.258 0.187 RF 0.287 0.211 0.471 0.185 GBM 0.271 0.205 0.303 0.155 LSTM† 0.249 0.194 0.612 — MLP† 0.275 0.212 0.362 — RGNN 0.291 0.242 0.459 0.171 RGNNL 0.228 0.180 0.566 0.140 RGNNOA 0.230 0.183 0.558 0.139
0.737 0.351 0.758 — — 0.997 0.997 0.989
North West — 2022 fl = 0.187, cl = 0.801 DLNM 0.587 0.491 0.484 0.410 RF 0.582 0.488 0.486 0.461 GBM 0.576 0.485 0.494 0.406 LSTM† 0.581 0.523 0.534 — MLP† 0.506 0.435 0.554 — RGNN 0.336 0.248 0.485 0.184 RGNNL 0.425 0.356 0.397 0.244 RGNNOA 0.397 0.320 0.446 0.223
0.307 0.071 0.272 — — 0.959 0.882 0.893
Yorkshire — 2018 fl = 0.215, cl = 0.743 DLNM 0.330 0.242 0.262 RF 0.289 0.212 0.459 GBM 0.275 0.206 0.295 LSTM† 0.239 0.182 0.618 MLP† 0.270 0.209 0.508 RGNN 0.319 0.270 0.403 RGNNL 0.265 0.213 0.539 RGNNOA 0.262 0.210 0.521
0.189 0.185 0.156 — — 0.185 0.157 0.153
0.721 0.351 0.783 — — 0.981 0.986 0.981
Yorkshire — 2022 fl = 0.215, cl = 0.743 DLNM 0.558 0.452 0.485
0.372
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Region Model
RMSE↓ MAE↓ Pearson↑ CRPS↓
Cov-90
0.536 0.532 0.545 0.535 0.312 0.375 0.351
0.408 0.358 — — 0.175 0.213 0.196
0.115 0.369 — — 0.953 0.934 0.923
East Midlands — 2018 fl = 0.221, cl = 0.716 DLNM 0.335 0.262 0.346 0.199 RF 0.290 0.218 0.425 0.190 GBM 0.283 0.212 0.335 0.162 LSTM† 0.240 0.188 0.618 — MLP† 0.279 0.221 0.526 — RGNN 0.256 0.210 0.503 0.150 RGNNL 0.226 0.184 0.551 0.136 RGNNOA 0.225 0.182 0.545 0.133
0.710 0.392 0.742 — — 0.986 0.989 0.986
East Midlands — 2022 fl = 0.222, cl = 0.718 DLNM 0.548 0.439 0.561 0.359 RF 0.535 0.432 0.454 0.402 GBM 0.537 0.433 0.340 0.353 LSTM† 0.553 0.469 0.358 — MLP† 0.539 0.457 0.482 — RGNN 0.339 0.254 0.495 0.184 RGNNL 0.415 0.342 0.396 0.237 RGNNOA 0.389 0.310 0.449 0.217
0.449 0.101 0.386 — — 0.945 0.866 0.868
West Midlands — 2018 fl = 0.202, cl = 0.751 DLNM 0.327 0.251 0.353 0.194 RF 0.291 0.218 0.529 0.192 GBM 0.288 0.215 0.426 0.165 LSTM† 0.253 0.205 0.683 — MLP† 0.247 0.193 0.555 — RGNN 0.238 0.193 0.519 0.144 RGNNL 0.214 0.173 0.562 0.133 RGNNOA 0.210 0.169 0.557 0.130
0.699 0.345 0.764 — — 1.000 1.000 1.000
West Midlands — 2022 fl = 0.202, cl = 0.751 DLNM 0.554 0.457 0.533 0.376 RF 0.541 0.450 0.530 0.420 GBM 0.539 0.447 0.469 0.369 LSTM† 0.559 0.497 0.460 —
0.375 0.068 0.325 —
RF GBM LSTM† MLP† RGNN RGNNL RGNNOA
0.436 0.435 0.467 0.456 0.235 0.309 0.278
0.433 0.447 0.435 0.437 0.442 0.347 0.404
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Region Model
RMSE↓ MAE↓ Pearson↑ CRPS↓
Cov-90
0.481 0.330 0.397 0.383
— 0.180 0.224 0.213
— 0.948 0.904 0.901
East of England — 2018 fl = 0.191, cl = 0.753 DLNM 0.319 0.238 0.348 0.182 RF 0.285 0.205 0.407 0.179 GBM 0.265 0.194 0.395 0.147 LSTM† 0.281 0.216 0.494 — MLP† 0.261 0.199 0.508 — RGNN 0.215 0.164 0.579 0.126 RGNNL 0.220 0.172 0.597 0.130 RGNNOA 0.220 0.168 0.590 0.127
0.742 0.378 0.769 — — 0.973 0.973 0.964
East of England — 2022 fl = 0.191, cl = 0.756 DLNM 0.445 0.359 0.571 0.290 RF 0.438 0.354 0.476 0.326 GBM 0.442 0.355 0.327 0.288 LSTM† 0.450 0.388 0.365 — MLP† 0.412 0.358 0.383 — RGNN 0.327 0.269 0.407 0.186 RGNNL 0.398 0.342 0.324 0.234 RGNNOA 0.383 0.325 0.373 0.224
0.496 0.153 0.447 — — 0.901 0.827 0.816
MLP† RGNN RGNNL RGNNOA
0.405 0.239 0.325 0.304
0.527 0.508 0.433 0.471
London — 2018 fl = 0.135, cl = 0.801 DLNM 0.201 0.159 0.375 RF 0.182 0.142 0.454 GBM 0.173 0.136 0.427 LSTM† 0.200 0.165 0.442 MLP† 0.183 0.145 0.525 RGNN 0.180 0.150 0.633 RGNNL 0.225 0.192 0.625 RGNNOA 0.190 0.160 0.629 London — 2022 fl = 0.134, cl = 0.819 DLNM 0.352 0.299 0.450 RF 0.347 0.301 0.459 GBM 0.343 0.294 0.363 LSTM† 0.351 0.320 0.466 MLP† 0.334 0.299 0.599 RGNN 0.366 0.328 0.471 RGNNL 0.420 0.381 0.448
0.119 0.123 0.101 — — 0.114 0.136 0.118
0.764 0.367 0.797 — — 1.000 1.000 1.000
0.243 0.279 0.239 — — 0.218 0.254
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Region Model
RMSE↓ MAE↓ Pearson↑ CRPS↓
RGNNOA 0.379
0.341
0.468
Cov-90
0.227
0.874
South East — 2018 fl = 0.157, cl = 0.807 DLNM 0.272 0.205 0.315 0.156 RF 0.246 0.181 0.383 0.156 GBM 0.232 0.172 0.370 0.130 LSTM† 0.275 0.199 0.300 — MLP† 0.252 0.200 0.442 — RGNN 0.198 0.154 0.519 0.119 RGNNL 0.202 0.161 0.530 0.121 RGNNOA 0.203 0.159 0.526 0.119
0.770 0.359 0.806 — — 0.986 0.984 0.975
South East — 2022 fl = 0.157, cl = 0.808 DLNM 0.466 0.382 0.569 0.314 RF 0.464 0.380 0.462 0.354 GBM 0.465 0.381 0.430 0.316 LSTM† 0.474 0.414 0.426 — MLP† 0.449 0.393 0.510 — RGNN 0.340 0.282 0.442 0.194 RGNNL 0.407 0.351 0.394 0.242 RGNNOA 0.412 0.354 0.418 0.247
0.419 0.126 0.356 — — 0.888 0.792 0.759
South West — 2018 fl = 0.213, cl = 0.740 DLNM 0.316 0.239 0.319 0.180 RF 0.279 0.205 0.469 0.177 GBM 0.263 0.195 0.439 0.147 LSTM† 0.266 0.193 0.518 — MLP† 0.258 0.191 0.510 — RGNN 0.244 0.196 0.543 0.141 RGNNL 0.231 0.178 0.580 0.134 RGNNOA 0.220 0.170 0.565 0.127
0.770 0.375 0.833 — — 0.970 0.984 0.981
South West — 2022 fl = 0.214, cl = 0.741 DLNM 0.570 0.462 0.544 0.378 RF 0.557 0.456 0.468 0.426 GBM 0.560 0.460 0.394 0.377 LSTM† 0.558 0.487 0.448 — MLP† 0.509 0.439 0.511 — RGNN 0.379 0.294 0.524 0.209 RGNNL 0.521 0.447 0.467 0.323 RGNNOA 0.441 0.362 0.505 0.259
0.430 0.090 0.361 — — 0.866 0.630 0.745
Wales — 2018 fl = 0.303, cl = 0.651 DLNM 0.451 0.345 0.376
0.701
0.265
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Region Model RF GBM LSTM† MLP† RGNN RGNNL RGNNOA
RMSE↓ MAE↓ Pearson↑ CRPS↓
Cov-90
0.386 0.380 0.340 0.361 0.310 0.272 0.279
0.291 0.288 0.271 0.295 0.246 0.216 0.219
0.474 0.411 0.611 0.615 0.534 0.616 0.610
0.257 0.219 — — 0.179 0.160 0.162
0.321 0.756 — — 0.973 0.989 0.981
Wales — 2022 fl = 0.302, cl = 0.651 DLNM 0.637 0.504 0.502 RF 0.612 0.483 0.543 GBM 0.607 0.480 0.490 LSTM† 0.610 0.546 0.475 MLP† 0.619 0.545 0.488 RGNN 0.412 0.302 0.499 RGNNL 0.486 0.399 0.413 RGNNOA 0.456 0.358 0.468
0.405 0.447 0.385 — — 0.219 0.277 0.252
0.496 0.142 0.461 — — 0.926 0.868 0.882
fl = Poisson RMSE noise floor; cl = Pearson ceiling. RGNNL = RGNN-LSOA; RGNNOA = RGNN-OA.
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Fig. 6. Vanilla DLNM curves for each UK region in our experiments. Important to note in contrast with the optimised curves below is the flat portion at moderate temperatures, with a ‘bump’ due to the combination of spline specification and heat risk falling below detectable SNR levels.
Heat-Mortality Risk with GNNs
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Fig. 7. DLNM curves for each UK region in our experiments, optimised by RGNNLAD.
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Fig. 8. DLNM curves for each UK region in our experiments, optimised by RGNNLSOA.
Heat-Mortality Risk with GNNs
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Fig. 9. DLNM curves for each UK region in our experiments, optimised by RGNN-OA.