mlsanityData to 7 Oct 2026

Physics-Informed Koopman Network

arXiv 2211.09419 ↗First posted 17 Nov 2022cs.LG math.AP math.DScited by 2

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Abstract (arXiv)

Koopman operator theory is receiving increased attention due to its promise to linearize nonlinear dynamics. Neural networks that are developed to represent Koopman operators have shown great success thanks to their ability to approximate arbitrarily complex functions. However, despite their great potential, they typically require large training data-sets either from measurements of a real system or from high-fidelity simulations. In this work, we propose a novel architecture inspired by physics-informed neural networks, which leverage automatic differentiation to impose the underlying physical laws via soft penalty constraints during model training. We demonstrate that it not only reduces the need of large training data-sets, but also maintains high effectiveness in approximating Koopman eigenfunctions.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 32 of its 91 references that are in the map. First posted on arXiv 17 Nov 2022.

Builds on

32 of 91 references.

References · 32

  1. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  2. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  3. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  4. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
  5. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
  6. 2021Physics-informed neural networks with hard constraints for inverse designcited by 277
  7. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  8. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  9. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  10. 2017Learning Koopman Invariant Subspaces for Dynamic Mode Decompositioncited by 156
  11. 2018Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problemscited by 144
  12. 2016Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive controlcited by 134
20 more
  1. 2014Dynamic mode decomposition with controlcited by 128
  2. 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 125
  3. 2018Adversarial Uncertainty Quantification in Physics-Informed Neural Networkscited by 120
  4. 2020Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEscited by 115
  5. 2020Forecasting Sequential Data using Consistent Koopman Autoencoderscited by 114
  6. 2021Parallel Physics-Informed Neural Networks via Domain Decompositioncited by 112
  7. 2018Deep Dynamical Modeling and Control of Unsteady Fluid Flowscited by 67
  8. 2019Learning Compositional Koopman Operators for Model-Based Controlcited by 67
  9. 2019Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networkscited by 63
  10. 2020NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation frameworkcited by 58
  11. 2020From Fourier to Koopman: Spectral Methods for Long-term Time Series Predictioncited by 50
  12. 2014Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decompositioncited by 49
  13. 2021Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networkscited by 43
  14. 2013Sparsity-promoting dynamic mode decompositioncited by 30
  15. 2020Deep Learning of Koopman Representation for Controlcited by 25
  16. 2019Deep Variational Koopman Models: Inferring Koopman Observations for Uncertainty-Aware Dynamics Modeling and Controlcited by 18
  17. 2015Compressed Dynamic Mode Decomposition for Background Modelingcited by 17
  18. 2019Deep Learning Models for Global Coordinate Transformations that Linearize PDEscited by 17
  19. 2014Dynamic Mode Decomposition for Real-Time Background/Foreground Separation in Videocited by 9
  20. 2021Extended dynamic mode decomposition with dictionary learning using neural ordinary differential equationscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 0; 2026: 1.

2 papers.

  1. 2024Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddingscited by 1
  2. 2026SPIKE: Sparse Koopman Regularization for Physics-Informed Neural Networkscited by 0