mlsanityData to 14 Oct 2026

Exactly conservative physics-informed neural networks and deep operator networks for dynamical systems

arXiv 2311.14131 ↗First posted 23 Nov 2023cs.LG cs.NA math.NAcited by 13

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Abstract (arXiv)

We introduce a method for training exactly conservative physics-informed neural networks and physics-informed deep operator networks for dynamical systems. The method employs a projection-based technique that maps a candidate solution learned by the neural network solver for any given dynamical system possessing at least one first integral onto an invariant manifold. We illustrate that exactly conservative physics-informed neural network solvers and physics-informed deep operator networks for dynamical systems vastly outperform their non-conservative counterparts for several real-world problems from the mathematical sciences.

Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). Builds on 17 of its 42 references that are in the map. First posted on arXiv 23 Nov 2023.

Builds on

17 of 42 references.

References · 17

  1. 2020Language Models are Few-Shot Learnerscited by 32,419
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2020Gradient Surgery for Multi-Task Learningcited by 1,256
  4. 2016Group Equivariant Convolutional Networkscited by 1,165
  5. 2019Hamiltonian Neural Networkscited by 712
  6. 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
  7. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  8. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 235
  9. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 187
  10. 2022Respecting causality is all you need for training physics-informed neural networkscited by 156
  11. 2022Physics-Informed Deep Neural Operator Networkscited by 113
  12. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 89
5 more
  1. 2021Physics-informed neural networks for the shallow-water equations on the spherecited by 32
  2. 2020Structure preserving deep learningcited by 31
  3. 2023Improving physics-informed neural networks with meta-learned optimizationcited by 19
  4. 2022Exact conservation laws for neural network integrators of dynamical systemscited by 15
  5. 2023Improving physics-informed DeepONets with hard constraintscited by 9

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 7; 2026: 5.

13 papers.

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  1. 2025Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Spacecited by 6
  2. 2024PinnDE: Physics-Informed Neural Networks for Solving Differential Equationscited by 1
  3. 2025Adaptive Correction for Ensuring Conservation Laws in Neural Operatorscited by 1
  4. 2025Physically consistent model learning for reaction-diffusion systemscited by 1
  5. 2026FluxNet: Learning Capacity-Constrained Local Transport Operators for Conservative and Bounded PDE Surrogatescited by 1
  6. 2026Physics-Informed Laplace Neural Operator for Solving Partial Differential Equationscited by 1
  7. 2025Improving regional weather forecasts with neural interpolationcited by 0
  8. 2025Low-rank adaptive physics-informed HyperDeepONets for solving differential equationscited by 0
  9. 2025Physics-Informed Operator Learning for Hemodynamic Modelingcited by 0
  10. 2025Guaranteeing Conservation of Integrals with Projection in Physics-Informed Neural Networkscited by 0
  11. 2026A Comparative Investigation of Thermodynamic Structure-Informed Neural Networkscited by 0
  12. 2026Stochastic Dimension Implicit Functional Projections for Global Integral Conservation in High-Dimensional PINNscited by 0
1 more
  1. 2026A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Lawscited by 0