On-chip partial differential equation solving based on physics-informed neural networks

Physics-Informed Neural Networks (PINNs) is a recently proposed deep learning framework that embeds the laws of physics into the network training process, thus enabling the solution of forward and inverse problems involving partial differential equations (PDEs). Traditional numerical methods are limited in their computational efficiency in solving high-dimensional PDEs. As a new methodology, PINNs can compute high-dimensional PDEs efficiently, but the computation cost is still high due to the large number of matrix operations and gradient computations. Photonic computing utilizes photonic parallelism to achieve high-speed, low-power matrix operations and is particularly suitable for accelerating linear computational bottlenecks in high-dimensional PDE solving. This research is focused on creating effective PDE solvers by combining PINNs with photonic chip technologies. The efficient combination seeks to greatly increase the efficiency of PDE solving by accelerating matrix operations and auto-differentiation procedures.