# Physics-informed Neural Networks to Model and Control Robots: a Theoretical and Experimental Investigation

arXiv: https://arxiv.org/abs/2305.05375 · HTML: https://mlsanity.com/paper/2305.05375/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2023.

## Built on by (most cited first, 17 of 17)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Neural Autoencoder-Based Structure-Preserving Model Order Reduction and Control Design for High-Dimensional Physical Systems](https://mlsanity.com/paper/2312.06256/) (2023)
- [Metamizer: a versatile neural optimizer for fast and accurate physics simulations](https://mlsanity.com/paper/2410.19746/) (2024)
- [Learning Low-Dimensional Strain Models of Soft Robots by Looking at the Evolution of Their Shape with Application to Model-Based Control](https://mlsanity.com/paper/2411.00138/) (2024)
- [Generalizable and Fast Surrogates: Model Predictive Control of Articulated Soft Robots using Physics-Informed Neural Networks](https://mlsanity.com/paper/2502.01916/) (2025)
- [Adaptive Model-Predictive Control of a Soft Continuum Robot Using a Physics-Informed Neural Network Based on Cosserat Rod Theory](https://mlsanity.com/paper/2508.12681/) (2025)
- [Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach](https://mlsanity.com/paper/2509.24627/) (2025)
- [Data-Driven Adaptive PID Control Based on Physics-Informed Neural Networks](https://mlsanity.com/paper/2510.04591/) (2025)
- [Learning Visually Interpretable Oscillator Networks for Soft Continuum Robots from Video](https://mlsanity.com/paper/2511.18322/) (2025)
- [Symbolic Learning of Interpretable Reduced-Order Models for Jumping Quadruped Robots](https://mlsanity.com/paper/2508.06538/) (2025)
- [QuietWalk: Physics-Informed Reinforcement Learning for Ground Reaction Force-Aware Humanoid Locomotion Under Diverse Footwear](https://mlsanity.com/paper/2604.23702/) (2026)
- [Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equations](https://mlsanity.com/paper/2605.06246/) (2026)
- [Learned Lyapunov Shielding for Adaptive Control](https://mlsanity.com/paper/2605.06934/) (2026)
- [CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts](https://mlsanity.com/paper/2607.06824/) (2026)
- [SoRoMoX: Fast, Differentiable, and Parallelizable Soft Robot Models](https://mlsanity.com/paper/2608.06650/) (2026)
- [Constraint-Aware Physics-Informed Neural Networks for Static Shape Estimation of Co-Manipulative Continuum Robots](https://mlsanity.com/paper/2608.26273/) (2026)
- [Seven Sources of Physical AI Capability Formation](https://mlsanity.com/paper/2609.09627/) (2026)

## Abstract (arXiv)

This work concerns the application of physics-informed neural networks to the modeling and control of complex robotic systems. Achieving this goal required extending Physics Informed Neural Networks to handle non-conservative effects. We propose to combine these learned models with model-based controllers originally developed with first-principle models in mind. By combining standard and new techniques, we can achieve precise control performance while proving theoretical stability bounds. These validations include real-world experiments of motion prediction with a soft robot and of trajectory tracking with a Franka Emika manipulator.