A Comparison of Strategies to Embed Physics-Informed Neural Networks in Nonlinear Model Predictive Control Formulations Solved via Direct Transcription

[2501.06335] A Comparison of Strategies to Embed Physics-Informed Neural Networks in Nonlinear Model Predictive Control Formulations Solved via Direct Transcription Skip to main content Search Submit Donate Log in Electrical Engineering and Systems Science > Systems and Control arXiv:2501.06335 (eess) [Submitted on 10 Jan 2025] Title: A Comparison of Strategies to Embed Physics-Informed Neural Networks in Nonlinear Model Predictive Control Formulations Solved via Direct Transcription Authors: Carlos Andrés Elorza Casas , Luis A. Ricardez-Sandoval , Joshua L. Pulsipher View PDF Abstract: This study aims to benchmark candidate strategies for embedding neural network (NN) surrogates in nonlinear model predictive control (NMPC) formulations that are subject to systems described with partial differential equations and that are solved via direct transcription (i.e., simultaneous methods). This study focuses on the use of physics-informed NNs and physics-informed convolutional NNs as the internal (surrogate) models within the NMPC formulation. One strategy embeds NN models as explicit algebraic constraints, leveraging the automatic differentiation (AD) of an algebraic modelling language (AML) to evaluate the derivatives. Alternatively, the solver can be provided with derivatives computed external to the AML via the AD routines of the machine learning environment the NN is trained in. The three numerical experiments considered in this work reveal that replacing mechanistic models with NN surrogates may not always offer computational advantages when smooth activation functions are used in conjunction with a local nonlinear solver (e.g., Ipopt), even with highly nonlinear systems. Moreover, in this context, the external function evaluation of the NN surrogates often outperforms the embedding strategies that rely on explicit algebraic constraints, likely due to the difficulty in initializing the auxiliary variables and constraints introduced by explicit algebraic reformulations. Subjects: Systems and Control (eess.SY) ; Optimization and Control (math.OC) Cite as: arXiv:2501.06335 [eess.SY] (or arXiv:2501.06335v1 [eess.SY] for this version) https://doi.org/10.48550/arXiv.2501.06335 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1016/j.compchemeng.2025.109105 Focus to learn more DOI(s) linking to related resources Submission history From: Joshua Pulsipher [ view email ] [v1] Fri, 10 Jan 2025 20:41:11 UTC (1,330 KB) Full-text links: Access Paper: View PDF view license Current browse context: eess.SY < prev | next > new | recent | 2025-01 Change to browse by: cs cs.SY eess math math.OC References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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