Good Lattice Accelerates Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) can solve partial differential equations (PDEs) by minimizing the physics-informed loss, ensuring the neural network satisfies the PDE at given points. However, the solutions to a PDE are infinite-dimensional, and the physics-informed loss is a finite approximation to a certain integral over the domain. This indicates that selecting appropriate points is essential. This paper proposes "good lattice training" (GLT), a technique inspired by number theoretic methods. GLT provides an optimal set of collocation points and can train PINNs to achieve competitive performance with smaller computational cost