FASTVPINNS: A FAST, VERSATILE AND ROBUST VARIATIONAL PINNS FRAMEWORK FOR FORWARD AND INVERSE PROBLEMS IN SCIENCE

Variational physics-informed neural networks (VPINNs), with h and p-refinement,show promise over conventional PINNs. But existing frameworks are computationally inefficient and unable to deal with complex meshes. As such, VPINNs have had limited application when it comes to practical problems in science andengineering. In the present work, we propose a novel VPINNs framework, thatachieves up to a 100x speed-up over SOTA codes. We demonstrate the flexibilityof this framework by solving different forward and inverse problems on complexgeometries, and by applying VPINNs to vector-valued partial differential equations.