# Physics-Informed Neural State Space Models via Learning and Evolution

arXiv: https://arxiv.org/abs/2011.13497 · HTML: https://mlsanity.com/paper/2011.13497/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2020.

## Built on by (most cited first, 9 of 9)

- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Constructing Neural Network-Based Models for Simulating Dynamical Systems](https://mlsanity.com/paper/2111.01495/) (2021)
- [Neural Ordinary Differential Equations for Nonlinear System Identification](https://mlsanity.com/paper/2203.00120/) (2022)
- [Auto-PINN: Understanding and Optimizing Physics-Informed Neural Architecture](https://mlsanity.com/paper/2205.13748/) (2022)
- [Meta-Learning of Neural State-Space Models Using Data From Similar Systems](https://mlsanity.com/paper/2211.07768/) (2022)
- [Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities](https://mlsanity.com/paper/2501.06572/) (2025)
- [A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic](https://mlsanity.com/paper/2204.06362/) (2022)
- [Meta-Learning for Physically-Constrained Neural System Identification](https://mlsanity.com/paper/2501.06167/) (2025)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)

## Abstract (arXiv)

Recent works exploring deep learning application to dynamical systems modeling have demonstrated that embedding physical priors into neural networks can yield more effective, physically-realistic, and data-efficient models. However, in the absence of complete prior knowledge of a dynamical system's physical characteristics, determining the optimal structure and optimization strategy for these models can be difficult. In this work, we explore methods for discovering neural state space dynamics models for system identification. Starting with a design space of block-oriented state space models and structured linear maps with strong physical priors, we encode these components into a model genome alongside network structure, penalty constraints, and optimization hyperparameters. Demonstrating the overall utility of the design space, we employ an asynchronous genetic search algorithm that alternates between model selection and optimization and obtains accurate physically consistent models of three physical systems: an aerodynamics body, a continuous stirred tank reactor, and a two tank interacting system.