mlsanityData to 14 Oct 2026

Physics guided neural networks for modelling of non-linear dynamics

arXiv 2205.06858 ↗First posted 13 May 2022cs.LG nlin.CDcited by 20

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Abstract (arXiv)

The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However, it is difficult to train these models on complex dynamical systems from data alone due to their low data efficiency and sensitivity to hyperparameters and initialisation. This work demonstrates that injection of partially known information at an intermediate layer in a DNN can improve model accuracy, reduce model uncertainty, and yield improved convergence during the training. The value of these physics-guided neural networks has been demonstrated by learning the dynamics of a wide variety of nonlinear dynamical systems represented by five well-known equations in nonlinear systems theory: the Lotka-Volterra, Duffing, Van der Pol, Lorenz, and Henon-Heiles systems.

Key facts. Cited by 20 papers in the map (data through 14 Oct 2026). Builds on 10 of its 71 references that are in the map. First posted on arXiv 13 May 2022.

Builds on

10 of 71 references.

References · 10

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  3. 2019Algorithms for Verifying Deep Neural Networkscited by 221
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  5. 2020A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applicationscited by 53
  6. 2020Physics guided machine learning using simplified theoriescited by 23
  7. 2021Deep neural network enabled corrective source term approach to hybrid analysis and modelingcited by 16
  8. 2021Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolutioncited by 14
  9. 2020Physics-Incorporated Convolutional Recurrent Neural Networks for Source Identification and Forecasting of Dynamical Systemscited by 12
  10. 2019Taming an autonomous surface vehicle for path following and collision avoidance using deep reinforcement learningcited by 9

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 4; 2023: 4; 2024: 5; 2025: 4; 2026: 3.

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  1. 2024State-space models are accurate and efficient neural operators for dynamical systemscited by 28
  2. 2024Physics Informed Kolmogorov-Arnold Neural Networks for Dynamical Analysis via Efficent-KAN and WAV-KANcited by 25
  3. 2023Towards Complex Dynamic Physics System Simulation with Graph Neural ODEscited by 8
  4. 2023Digital Twins in Wind Energy: Emerging Technologies and Industry-Informed Future Directionscited by 7
  5. 2023Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applicationscited by 7
  6. 2022Combining physics-based and data-driven techniques for reliable hybrid analysis and modeling using the corrective source term approachcited by 6
  7. 2022A novel corrective-source term approach to modeling unknown physics in aluminum extraction processcited by 4
  8. 2023Randomized prior wavelet neural operator for uncertainty quantificationcited by 4
  9. 2022Decentralized digital twins of complex dynamical systemscited by 2
  10. 2024Point Neuron Learning: A New Physics-Informed Neural Network Architecturecited by 2
  11. 2022Machine Learning for Smart and Energy-Efficient Buildingscited by 1
  12. 2025Unified Spatiotemporal Physics-Informed Learning (USPIL): A Framework for Modeling Complex Predator-Prey Dynamicscited by 1
8 more
  1. 2024A novel framework for generalization of deep hidden physics modelscited by 0
  2. 2024Aeroengine performance prediction using a physical-embedded data-driven methodcited by 0
  3. 2025Enhanced accuracy through ensembling of randomly initialized auto-regressive models for time-dependent PDEscited by 0
  4. 2025Learning with Mandelbrot and Juliacited by 0
  5. 2025Enabling Physical AI at the Edge: Hardware-Accelerated Recovery of System Dynamicscited by 0
  6. 2026Hamiltonian Graph Inference Networks: Joint structure discovery and dynamics prediction for lattice Hamiltonian systems from trajectory datacited by 0
  7. 2026Geometric Kolmogorov--Arnold Network (GeoKAN)cited by 0
  8. 2026Neural Operator based Multi-Field Reconstruction of Inner Solar Boundary Statecited by 0