mlsanityData to 14 Oct 2026

PINN Balls: Scaling Second-Order Methods for PINNs with Domain Decomposition and Adaptive Sampling

arXiv 2510.21262 ↗First posted 24 Oct 2025cs.LGcited by 0

On the map: Mixture-of-experts → MoE theory and gating functions

Abstract (arXiv)

Recent advances in Scientific Machine Learning have shown that second-order methods can enhance the training of Physics-Informed Neural Networks (PINNs), making them a suitable alternative to traditional numerical methods for Partial Differential Equations (PDEs). However, second-order methods induce large memory requirements, making them scale poorly with the model size. In this paper, we define a local Mixture of Experts (MoE) combining the parameter-efficiency of ensemble models and sparse coding to enable the use of second-order training. Our model -- textscPINN Balls -- also features a fully learnable domain decomposition structure, achieved through the use of Adversarial Adaptive Sampling (AAS), which adapts the DD to the PDE and its domain. textscPINN Balls achieves better accuracy than the state-of-the-art in scientific machine learning, while maintaining invaluable scalability properties and drawing from a sound theoretical background.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts. Builds on 13 of its 39 references that are in the map. First posted on arXiv 24 Oct 2025.

Builds on

13 of 39 references.

References · 13

  1. 2017Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layercited by 3,509
  2. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  3. 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
  4. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  5. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  6. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 235
  7. 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 145
  8. 2021Parallel Physics-Informed Neural Networks via Domain Decompositioncited by 112
  9. 2022Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodologycited by 44
  10. 2022Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustrationcited by 21
  11. 2024The Challenges of the Nonlinear Regime for Physics-Informed Neural Networkscited by 21
  12. 2023Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEscited by 18
1 more
  1. 2022Meta Learning of Interface Conditions for Multi-Domain Physics-Informed Neural Networkscited by 6

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2025RL-PINNs: Reinforcement Learning-Driven Adaptive Sampling for Efficient Training of PINNs
  2. 2025S2GPT-PINNs: Sparse and Small models for PDEs
  3. 2026Unlearning Noise in PINNs: A Selective Pruning Framework for PDE Inverse Problems
  4. 2025Sub-Sequential Physics-Informed Learning with State Space Model
  5. 2025Tensor-Compressed and Fully-Quantized Training of Neural PDE Solvers
  6. 2025KD-PINN: Knowledge-Distilled PINNs for ultra-low-latency real-time neural PDE solvers
  7. 2024Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts
  8. 2023LatentPINNs: Generative physics-informed neural networks via a latent representation learning