Scaling physics-informed hard constraints with mixture-of-experts

arXiv:2402.13412v1 Announce Type: new
Abstract: Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, reliability, convergence, and data efficiency for modeling physical dynamics. While such constraints can be softly imposed via loss function penalties, recent advancements in differentiable physics and optimization improve performance by incorporating PDE-constrained optimization as individual layers in neural networks. This enables a stricter adherence to physical constraints. However, imposing hard constraints significantly increases computational and …

abstract accuracy arxiv bias conservation constraints convergence cs.ai cs.lg cs.na data differentiable dynamics efficiency experts function inductive laws loss math.na math.oc modeling network network training neural network optimization performance physics physics-informed reliability scaling training type via