Experimental Demonstration of an Optical Neural PDE Solver via On-Chip PINN Training

Examples include electromagnetic modeling and thermal analysis of IC chips [1], medical imaging [2], safety verification of autonomous systems [3]. Discretization-based solvers (e.g., finite-difference and finite-element methods) convert a PDE to a large-scale algebraic equation via spatial and temporal discretization. Solving the resulting algebraic equation often requires massive digital resources and run times. Physics-informed neural network (PINN) is a promising discretization-free and unsupervised approach to solve PDEs [4]. PINN uses the residuals of a PDE operator and the boundary/initial conditions to set up a loss function, then minimizes the loss to train a neural network as a global approximation of the PDE solution. However, current PINN training typically needs several to dozens of hours on a powerful GPU, hindering the deployment of an real-time neural PDE solver on edge devices.