Physically Consistent Neural ODEs for Learning Multi-Physics Systems

• URL: http://arxiv.org/abs/2211.06130v1
• Date: Fri, 11 Nov 2022 11:20:35 GMT
• Title: Physically Consistent Neural ODEs for Learning Multi-Physics Systems
• Authors: Muhammad Zakwan, Loris Di Natale, Bratislav Svetozarevic, Philipp Heer, Colin N. Jones, and Giancarlo Ferrari Trecate
• Abstract summary: In this paper, we leverage the framework of Irreversible port-Hamiltonian Systems (IPHS), which can describe most multi-physics systems. We propose Physically Consistent NODEs (PC-NODEs) to learn parameters from data. We demonstrate the effectiveness of the proposed method by learning the thermodynamics of a building from the real-world measurements.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Despite the immense success of neural networks in modeling system dynamics from data, they often remain physics-agnostic black boxes. In the particular case of physical systems, they might consequently make physically inconsistent predictions, which makes them unreliable in practice. In this paper, we leverage the framework of Irreversible port-Hamiltonian Systems (IPHS), which can describe most multi-physics systems, and rely on Neural Ordinary Differential Equations (NODEs) to learn their parameters from data. Since IPHS models are consistent with the first and second principles of thermodynamics by design, so are the proposed Physically Consistent NODEs (PC-NODEs). Furthermore, the NODE training procedure allows us to seamlessly incorporate prior knowledge of the system properties in the learned dynamics. We demonstrate the effectiveness of the proposed method by learning the thermodynamics of a building from the real-world measurements and the dynamics of a simulated gas-piston system. Thanks to the modularity and flexibility of the IPHS framework, PC-NODEs can be extended to learn physically consistent models of multi-physics distributed systems.

Related papers

• Learning System Dynamics without Forgetting [60.08612207170659]
  Predicting trajectories of systems with unknown dynamics is crucial in various research fields, including physics and biology. We present a novel framework of Mode-switching Graph ODE (MS-GODE), which can continually learn varying dynamics. We construct a novel benchmark of biological dynamic systems, featuring diverse systems with disparate dynamics.
  arXiv  Detail & Related papers  (2024-06-30T14:55:18Z)
• Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics [97.38308257547186]
  Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and material models. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. We introduce a new framework termed "Neural Constitutive Laws" (NCLaw) which utilizes a network architecture that strictly guarantees standard priors.
  arXiv  Detail & Related papers  (2023-04-27T17:42:24Z)
• ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Prediction [82.81767856234956]
  This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling. We show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics.
  arXiv  Detail & Related papers  (2023-02-11T21:07:30Z)
• Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations [68.62843292346813]
  We propose a structured latent ODE model that captures system input variations within its latent representation. Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
  arXiv  Detail & Related papers  (2022-02-25T20:00:56Z)
• Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
  Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
  arXiv  Detail & Related papers  (2021-11-02T10:51:42Z)
• Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertainty [6.151348127802708]
  We propose a physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM) The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system.
  arXiv  Detail & Related papers  (2021-10-16T16:35:12Z)
• Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling [19.399031618628864]
  We develop a framework to learn dynamics models from trajectory data. We place constraints on the values of the outputs and the internal states of the model. We experimentally demonstrate the benefits of the proposed approach on a variety of dynamical systems.
  arXiv  Detail & Related papers  (2021-09-14T02:47:51Z)
• Encoding physics to learn reaction-diffusion processes [18.187800601192787]
  We show how a deep learning framework that encodes given physics structure can be applied to a variety of problems regarding the PDE system regimes. The resultant learning paradigm that encodes physics shows high accuracy, robustness, interpretability and generalizability demonstrated via extensive numerical experiments.
  arXiv  Detail & Related papers  (2021-06-09T03:02:20Z)
• Hard Encoding of Physics for Learning Spatiotemporal Dynamics [8.546520029145853]
  We propose a deep learning architecture that forcibly encodes known physics knowledge to facilitate learning in a data-driven manner. The coercive encoding mechanism of physics, which is fundamentally different from the penalty-based physics-informed learning, ensures the network to rigorously obey given physics.
  arXiv  Detail & Related papers  (2021-05-02T21:40:39Z)
• Neural Dynamical Systems: Balancing Structure and Flexibility in Physical Prediction [14.788494279754481]
  We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings. NDS uses neural networks to estimate free parameters of the system, predicts residual terms, and numerically integrates over time to predict future states.
  arXiv  Detail & Related papers  (2020-06-23T00:50:48Z)
• Learning Stable Deep Dynamics Models [91.90131512825504]
  We propose an approach for learning dynamical systems that are guaranteed to be stable over the entire state space. We show that such learning systems are able to model simple dynamical systems and can be combined with additional deep generative models to learn complex dynamics.
  arXiv  Detail & Related papers  (2020-01-17T00:04:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.