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Physics-Informed Neural Nets for Control of Dynamical Systems

arXiv 2104.02556 ↗First posted 6 Apr 2021cs.LGcited by 31

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Abstract (arXiv)

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by Ordinary Differential Equations (ODEs), the conventional PINN has a continuous time input variable and outputs the solution of the corresponding ODE. In their original form, PINNs do not allow control inputs, neither can they simulate for variable long-range intervals without serious degradation in their predictions. In this context, this work presents a new framework called Physics-Informed Neural Nets for Control (PINC), which proposes a novel PINN-based architecture that is amenable to control problems and able to simulate for longer-range time horizons that are not fixed beforehand, making it a very flexible framework when compared to traditional PINNs. Furthermore, this long-range time simulation of differential equations is faster than numerical methods since it relies only on signal propagation through the network, making it less computationally costly and, thus, a better alternative for simulation of models in Model Predictive Control. We showcase our proposal in the control of two nonlinear dynamic systems: the Van der Pol oscillator and the four-tank system.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). Builds on 13 of its 63 references that are in the map. First posted on arXiv 6 Apr 2021.

Builds on

13 of 63 references.

References · 13

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2019Optuna: A Next-generation Hyperparameter Optimization Frameworkcited by 2,455
  4. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  5. 2014Deeply-Supervised Netscited by 364
  6. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
  7. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
  8. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  9. 2019PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEscited by 116
  10. 2019Physics Informed Extreme Learning Machine (PIELM) -- A rapid method for the numerical solution of partial differential equationscited by 66
  11. 2018Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equationscited by 54
  12. 2018Learning an Approximate Model Predictive Controller with Guaranteescited by 54
1 more
  1. 2019Enforcing constraints for time series prediction in supervised, unsupervised and reinforcement learningcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 4; 2023: 1; 2024: 10; 2025: 12; 2026: 4.

31 papers.

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  1. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  2. 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 43
  3. 2022Physics-informed neural networks for PDE-constrained optimization and controlcited by 19
  4. 2022RAMP-Net: A Robust Adaptive MPC for Quadrotors via Physics-informed Neural Networkcited by 12
  5. 2025Deep Operator Networks for Bayesian Parameter Estimation in PDEscited by 6
  6. 2026Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operatorscited by 6
  7. 2024Physics-Informed Neural Networks with Skip Connections for Modeling and Control of Gas-Lifted Oil Wellscited by 4
  8. 2024Domain-decoupled Physics-informed Neural Networks with Closed-form Gradients for Fast Model Learning of Dynamical Systemscited by 4
  9. 2024Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order modelscited by 4
  10. 2025Generalizable and Fast Surrogates: Model Predictive Control of Articulated Soft Robots using Physics-Informed Neural Networkscited by 3
  11. 2025Adaptive Model-Predictive Control of a Soft Continuum Robot Using a Physics-Informed Neural Network Based on Cosserat Rod Theorycited by 3
  12. 2023Actor-Critic Methods using Physics-Informed Neural Networks: Control of a 1D PDE Model for Fluid-Cooled Battery Packscited by 2
19 more
  1. 2024Common pitfalls to avoid while using multiobjective optimization in machine learningcited by 2
  2. 2024Gradient Flow Based Phase-Field Modeling Using Separable Neural Networkscited by 1
  3. 2024Solving Differential Equations using Physics-Informed Deep Equilibrium Modelscited by 1
  4. 2024Physics-Informed Machine Learning for Grade Prediction in Froth Flotationcited by 1
  5. 2024Robust Neural IDA-PBC: passivity-based stabilization under approximationscited by 1
  6. 2025MILP initialization for solving parabolic PDEs with PINNscited by 1
  7. 2025Data-Driven Adaptive PID Control Based on Physics-Informed Neural Networkscited by 1
  8. 2025Tensor-Compressed and Fully-Quantized Training of Neural PDE Solverscited by 1
  9. 2024Receding Hamiltonian-Informed Optimal Neural Control and State Estimation for Closed-Loop Dynamical Systemscited by 0
  10. 2024Latent feedback control of distributed systems in multiple scenarios through deep learning-based reduced order modelscited by 0
  11. 2025Acoustic Wave Manipulation Through Sparse Robotic Actuationcited by 0
  12. 2025A Low-complexity Structured Neural Network to Realize States of Dynamical Systemscited by 0
  13. 2025Modelling of Underwater Vehicles using Physics-Informed Neural Networks with Controlcited by 0
  14. 2025Physics-Informed Neural Networks for Control of Single-Phase Flow Systems Governed by Partial Differential Equationscited by 0
  15. 2025Learning Robust Satellite Attitude Dynamics with Physics-Informed Normalising Flowcited by 0
  16. 2025PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehiclescited by 0
  17. 2026Learned Lyapunov Shielding for Adaptive Controlcited by 0
  18. 2026Hierarchical Causal Abduction: A Foundation Framework for Explainable Model Predictive Controlcited by 0
  19. 2026Real-time optimal control with shallow recurrent decoder networkscited by 0