{"ID":2850538,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.21262","arxiv_id":"2510.21262","title":"PINN Balls: Scaling Second-Order Methods for PINNs with Domain Decomposition and Adaptive Sampling","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 -- \\textsc{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. \\textsc{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.","short_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 requi...","url_abs":"https://arxiv.org/abs/2510.21262","url_pdf":"https://arxiv.org/pdf/2510.21262v1","authors":"[\"Andrea Bonfanti\",\"Ismael Medina\",\"Roman List\",\"Björn Staeves\",\"Roberto Santana\",\"Marco Ellero\"]","published":"2025-10-24T08:48:44Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Mixture of Experts\"]","has_code":false}