NAPI-MPC: Neural Accelerated Physics-Informed MPC for Nonlinear PDE Systems

Peilun Li, Kaiyuan Tan, Thomas Beckers
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:1230-1242, 2025.

Abstract

The control of systems governed by nonlinear partial differential equations (PDEs) can present substantial challenges for traditional linear model predictive control (MPC) approaches. Data-driven MPC has emerged as a solution for dealing with unknown nonlinear dynamics, but issues regarding safety guarantees, accuracy, and data efficiency remain a concern. We propose NAPI-MPC: a novel physics-informed scenario-based MPC approach for control of nonlinear PDE systems with partially unknown dynamics. Unlike other physics-informed learning methods that require extensive knowledge on the governing equations, our NAPI-MPC leverages distributed Port-Hamiltonian systems as a generalized, energy-based representation of the PDE dynamics, in which the Hamiltonian is modeled and learned by a Gaussian process. The Bayesian nature of the Gaussian process enables the drawing of scenario samples that are used in scenario-based predictive control to determine the optimal control action for the PDE system. To ensure applicability in time-sensitive contexts, we leverage a neural network as proxy for the MPC controller, trained offline on states and optimal control actions to enable fast inference for real-time operation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v283-li25d, title = {NAPI-MPC: Neural Accelerated Physics-Informed MPC for Nonlinear PDE Systems}, author = {Li, Peilun and Tan, Kaiyuan and Beckers, Thomas}, booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference}, pages = {1230--1242}, year = {2025}, editor = {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro}, volume = {283}, series = {Proceedings of Machine Learning Research}, month = {04--06 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v283/main/assets/li25d/li25d.pdf}, url = {https://proceedings.mlr.press/v283/li25d.html}, abstract = {The control of systems governed by nonlinear partial differential equations (PDEs) can present substantial challenges for traditional linear model predictive control (MPC) approaches. Data-driven MPC has emerged as a solution for dealing with unknown nonlinear dynamics, but issues regarding safety guarantees, accuracy, and data efficiency remain a concern. We propose NAPI-MPC: a novel physics-informed scenario-based MPC approach for control of nonlinear PDE systems with partially unknown dynamics. Unlike other physics-informed learning methods that require extensive knowledge on the governing equations, our NAPI-MPC leverages distributed Port-Hamiltonian systems as a generalized, energy-based representation of the PDE dynamics, in which the Hamiltonian is modeled and learned by a Gaussian process. The Bayesian nature of the Gaussian process enables the drawing of scenario samples that are used in scenario-based predictive control to determine the optimal control action for the PDE system. To ensure applicability in time-sensitive contexts, we leverage a neural network as proxy for the MPC controller, trained offline on states and optimal control actions to enable fast inference for real-time operation.} }
Endnote
%0 Conference Paper %T NAPI-MPC: Neural Accelerated Physics-Informed MPC for Nonlinear PDE Systems %A Peilun Li %A Kaiyuan Tan %A Thomas Beckers %B Proceedings of the 7th Annual Learning for Dynamics \& Control Conference %C Proceedings of Machine Learning Research %D 2025 %E Necmiye Ozay %E Laura Balzano %E Dimitra Panagou %E Alessandro Abate %F pmlr-v283-li25d %I PMLR %P 1230--1242 %U https://proceedings.mlr.press/v283/li25d.html %V 283 %X The control of systems governed by nonlinear partial differential equations (PDEs) can present substantial challenges for traditional linear model predictive control (MPC) approaches. Data-driven MPC has emerged as a solution for dealing with unknown nonlinear dynamics, but issues regarding safety guarantees, accuracy, and data efficiency remain a concern. We propose NAPI-MPC: a novel physics-informed scenario-based MPC approach for control of nonlinear PDE systems with partially unknown dynamics. Unlike other physics-informed learning methods that require extensive knowledge on the governing equations, our NAPI-MPC leverages distributed Port-Hamiltonian systems as a generalized, energy-based representation of the PDE dynamics, in which the Hamiltonian is modeled and learned by a Gaussian process. The Bayesian nature of the Gaussian process enables the drawing of scenario samples that are used in scenario-based predictive control to determine the optimal control action for the PDE system. To ensure applicability in time-sensitive contexts, we leverage a neural network as proxy for the MPC controller, trained offline on states and optimal control actions to enable fast inference for real-time operation.
APA
Li, P., Tan, K. & Beckers, T.. (2025). NAPI-MPC: Neural Accelerated Physics-Informed MPC for Nonlinear PDE Systems. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:1230-1242 Available from https://proceedings.mlr.press/v283/li25d.html.

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