Our paper was accepted at NeurIPS! - PINN Balls. Scaling Second-Order Methods for PINNs with Domain Decomposition and Adaptive Sampling

Phisics-Informed Neural Networks (PINNs) are a class of deep learning architecture specifically designed to solve Partial Differential Equations (PDEs). Despite the rapid development shown in recent years, several obstacles remain in the generalization capabilities of PINNs, as well as regarding their convergence behavior.

Our work proposes PINN Balls, a Mixture of Experts combining Second Order Methods (which allows for a faster training), Domain Decomposition (which increases the sparsity of the neural network and makes the Second Order Methods tractable) and Adversarial Adaptive Sampling (which focuses the attention of the PINN on difficult areas of the PDE 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.