PINN Balls: Scaling Second-Order Methods for PINNs with Domain Decomposition and Adaptive Sampling
Andrea Bonfanti, Ismael Medina, Roman List, Björn Staeves, Roberto Santana, Marco Ellero
Abstract
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 -- PINN 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. PINN 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.
BibTeX
@inproceedings{
bonfanti2025pinn,
title={{PINN} Balls: Scaling Second-Order Methods for {PINN}s with Domain Decomposition and Adaptive Sampling},
author={Andrea Bonfanti and Ismael Medina and Roman List and Bj{\"o}rn Staeves and Roberto Santana and Marco Ellero},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=xhKsnxJ9FD}
}