mlsanityData to 7 Oct 2026

Improving physics-informed DeepONets with hard constraints

arXiv 2309.07899 ↗First posted 14 Sep 2023cs.LG cs.NA math.NAcited by 9

Not on the map. Why?

Abstract (arXiv)

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods involve such conditions in computations without needing to learn them. In this study, we propose to improve current physics-informed deep learning strategies such that initial and/or boundary conditions do not need to be learned and are represented exactly in the predicted solution. Moreover, this method guarantees that when a deep operator network is applied multiple times to time-step a solution of an initial value problem, the resulting function is at least continuous.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 16 of its 27 references that are in the map. First posted on arXiv 14 Sep 2023.

Builds on

16 of 27 references.

References · 16

  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  2. 2015Automatic differentiation in machine learning: a surveycited by 846
  3. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  4. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  5. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
  6. 2021Physics-informed neural networks with hard constraints for inverse designcited by 277
  7. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 233
  8. 2022Respecting causality is all you need for training physics-informed neural networkscited by 154
  9. 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 142
  10. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
  11. 2020A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networkscited by 86
  12. 2021Improved architectures and training algorithms for deep operator networkscited by 85
4 more
  1. 2021Physics-informed neural networks for the shallow-water equations on the spherecited by 32
  2. 2023Improving physics-informed neural networks with meta-learned optimizationcited by 19
  3. 2023Deep-OSG: Deep Learning of Operators in Semigroupcited by 9
  4. 2023M-ENIAC: A machine learning recreation of the first successful numerical weather forecastscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 3; 2025: 3; 2026: 2.

9 papers.

  1. 2023Exactly conservative physics-informed neural networks and deep operator networks for dynamical systemscited by 13
  2. 2024Neural Parameter Regression for Explicit Representations of PDE Solution Operatorscited by 1
  3. 2024PinnDE: Physics-Informed Neural Networks for Solving Differential Equationscited by 1
  4. 2025Physics-Informed Deep B-Spline Networkscited by 1
  5. 2025Neural Spline Operators for Risk Quantification in Stochastic Systemscited by 1
  6. 2024Fredholm Integral Equations Neural Operator (FIE-NO) for Data-Driven Boundary Value Problemscited by 0
  7. 2025Low-rank adaptive physics-informed HyperDeepONets for solving differential equationscited by 0
  8. 2026Deep Operator Networks for Surrogate Modeling of Cyclic Adsorption Processes with Varying Initial Conditionscited by 0
  9. 2026The limits of exactness: On the failure of automatic differentiation in physics-informed machine learningcited by 0