mlsanityData to 7 Oct 2026

Optimal time sampling in physics-informed neural networks

arXiv 2404.18780 ↗First posted 29 Apr 2024cs.LG cs.NA math.NAcited by 3

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Abstract (arXiv)

Physics-informed neural networks (PINN) is a extremely powerful paradigm used to solve equations encountered in scientific computing applications. An important part of the procedure is the minimization of the equation residual which includes, when the equation is time-dependent, a time sampling. It was argued in the literature that the sampling need not be uniform but should overweight initial time instants, but no rigorous explanation was provided for this choice. In the present work we take some prototypical examples and, under standard hypothesis concerning the neural network convergence, we show that the optimal time sampling follows a (truncated) exponential distribution. In particular we explain when is best to use uniform time sampling and when one should not. The findings are illustrated with numerical examples on linear equation, Burgers' equation and the Lorenz system.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 9 of its 19 references that are in the map. First posted on arXiv 29 Apr 2024.

Builds on

9 of 19 references.

References · 9

  1. 2022Respecting causality is all you need for training physics-informed neural networkscited by 154
  2. 2020Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networkscited by 122
  3. 2020On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problemscited by 79
  4. 2023Tackling the Curse of Dimensionality with Physics-Informed Neural Networkscited by 78
  5. 2019Convergence rates for the stochastic gradient descent method for non-convex objective functionscited by 66
  6. 2023A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositionscited by 48
  7. 2022Adaptive Self-supervision Algorithms for Physics-informed Neural Networkscited by 24
  8. 2021The convergence of the Stochastic Gradient Descent (SGD) : a self-contained proofcited by 9
  9. 2024Convergence of a L2 regularized Policy Gradient Algorithm for the Multi Armed Banditcited by 2

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Cited by year

Citing papers per year: 2024: 1; 2025: 2.

3 papers.

  1. 2025Active Learning with Selective Time-Step Acquisition for PDEscited by 4
  2. 2024Regime-Aware Time Weighting for Physics-Informed Neural Networkscited by 0
  3. 2025Auto-Adaptive PINNs with Applications to Phase Transitionscited by 0