mlsanityData to 14 Oct 2026

Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems

arXiv 2306.13867 ↗First posted 24 Jun 2023eess.SY cs.LG cs.SYcited by 28

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Abstract (arXiv)

Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, PIML models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, PIML models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of PIML is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in PIML for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of PIML models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). Builds on 148 of its 231 references that are in the map. First posted on arXiv 24 Jun 2023.

Builds on

148 of 231 references.

References · 148

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50 most cited of 148 All 148 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 11; 2025: 12; 2026: 3.

28 papers.

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  1. 2024DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systemscited by 30
  2. 2025A roadmap for AI in roboticscited by 7
  3. 2024Learning Neural Differential Algebraic Equations via Operator Splittingcited by 6
  4. 2023Learning Dissipative Neural Dynamical Systemscited by 5
  5. 2024Multi-fidelity physics constrained neural networks for dynamical systemscited by 5
  6. 2024Morphological-Symmetry-Equivariant Heterogeneous Graph Neural Network for Robotic Dynamics Learningcited by 5
  7. 2025BONSAI: Structure-exploiting robust Bayesian optimization for networked black-box systems under uncertaintycited by 5
  8. 2024CAGES: Cost-Aware Gradient Entropy Search for Efficient Local Multi-Fidelity Bayesian Optimizationcited by 4
  9. 2024Domain-decoupled Physics-informed Neural Networks with Closed-form Gradients for Fast Model Learning of Dynamical Systemscited by 4
  10. 2024Combining Federated Learning and Control: A Surveycited by 3
  11. 2025Generalizable and Fast Surrogates: Model Predictive Control of Articulated Soft Robots using Physics-Informed Neural Networkscited by 3
  12. 2024Building Hybrid B-Spline And Neural Network Operatorscited by 2
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  1. 2024Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approachcited by 2
  2. 2025Manifold meta-learning for reduced-complexity neural system identificationcited by 2
  3. 2025Zero-Shot Transferable Solution Method for Parametric Optimal Control Problemscited by 2
  4. 2024Gait Switching and Enhanced Stabilization of Walking Robots with Deep Learning-based Reachability: A Case Study on Two-link Walkercited by 1
  5. 2025Data-Driven Adaptive PID Control Based on Physics-Informed Neural Networkscited by 1
  6. 2026Learnable Koopman-Enhanced Transformer-Based Time Series Forecasting with Spectral Controlcited by 1
  7. 2026Neural Operators for Multi-Task Control and Adaptationcited by 1
  8. 2023One-shot backpropagation for multi-step prediction in physics-based system identification -- EXTENDED VERSIONcited by 0
  9. 2024(Un)supervised Learning of Maximal Lyapunov Functionscited by 0
  10. 2025Predictive Modeling and Uncertainty Quantification of Fatigue Life in Metal Alloys using Machine Learningcited by 0
  11. 2025DeepKoopFormer: A Koopman Enhanced Transformer Based Architecture for Time Series Forecastingcited by 0
  12. 2025Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurementscited by 0
  13. 2025Control of dynamical systems with neural networkscited by 0
  14. 2025Sparse and nonparametric estimation of equations governing dynamical systems with applications to biologycited by 0
  15. 2025Direct transfer of optimized controllers to similar systems using dimensionless MPCcited by 0
  16. 2026Advancing multi-site emission control: A physics-informed transfer learning framework with mixture of experts for carbon-pollutant synergycited by 0