Learning the solution operator of a nonlinear parabolic equation using physics informed deep operator network (2308.11133v1)

Abstract: This study focuses on addressing the challenges of solving analytically intractable differential equations that arise in scientific and engineering fields such as Hamilton-Jacobi-BeLLMan. Traditional numerical methods and neural network approaches for solving such equations often require independent simulation or retraining when the underlying parameters change. To overcome this, this study employs a physics-informed DeepONet (PI-DeepONet) to approximate the solution operator of a nonlinear parabolic equation. PI-DeepONet integrates known physics into a deep neural network, which learns the solution of the PDE.