# Physically Consistent Neural ODEs for Learning Multi-Physics Systems

arXiv: https://arxiv.org/abs/2211.06130 · HTML: https://mlsanity.com/paper/2211.06130/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 20 references that are in the map.
- First posted on arXiv 11 Nov 2022.

## Builds on (most cited first, 13 of 13)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints](https://mlsanity.com/paper/2010.13581/) (2020)
- [Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming](https://mlsanity.com/paper/1903.01287/) (2019)
- [Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks](https://mlsanity.com/paper/2012.03133/) (2020)
- [Hamiltonian Deep Neural Networks Guaranteeing Non-vanishing Gradients by Design](https://mlsanity.com/paper/2105.13205/) (2021)
- [Physically Consistent Neural Networks for building thermal modeling: theory and analysis](https://mlsanity.com/paper/2112.03212/) (2021)
- [Robust Classification using Contractive Hamiltonian Neural ODEs](https://mlsanity.com/paper/2203.11805/) (2022)
- [On Energy Conversion in Port-Hamiltonian Systems](https://mlsanity.com/paper/2103.09116/) (2021)

## Built on by (most cited first, 3 of 3)

- [Towards Scalable Physically Consistent Neural Networks: an Application to Data-driven Multi-zone Thermal Building Models](https://mlsanity.com/paper/2212.12380/) (2022)
- [Learning Adaptive Hydrodynamic Models Using Neural ODEs in Complex Conditions](https://mlsanity.com/paper/2410.00490/) (2024)
- [Universal Approximation Property of Hamiltonian Deep Neural Networks](https://mlsanity.com/paper/2303.12147/) (2023)

## Abstract (arXiv)

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.