Optical Neural Engine for Solving Scientific Partial Differential Equations

TL;DR

This paper introduces an optical neural engine that leverages diffractive optical neural networks and optical crossbar structures to efficiently solve various partial differential equations, offering high-speed, low-energy, and reconfigurable computation for scientific applications.

Contribution

The paper presents the first optical neural engine architecture combining Fourier space and real space optical processing for solving diverse PDEs, demonstrating both numerical and experimental success.

Findings

Outperforms traditional PDE solvers in speed and energy efficiency

Comparable accuracy to state-of-the-art machine learning models

Supports real-time reconfigurability for multiple tasks

Abstract

Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data-driven machine learning (ML) approaches are emerging to accelerate time-consuming and computation-intensive numerical simulations of PDEs. Although optical systems offer high-throughput and energy-efficient ML hardware, there is no demonstration of utilizing them for solving PDEs. Here, we present an optical neural engine (ONE) architecture combining diffractive optical neural networks for Fourier space processing and optical crossbar structures for real space processing to solve time-dependent and time-independent PDEs in diverse disciplines, including Darcy flow equation, the magnetostatic Poisson equation in demagnetization, the Navier-Stokes equation in incompressible fluid, Maxwell's equations in nanophotonic metasurfaces, and coupled PDEs in a multiphysics system. We numerically and experimentally demonstrate the capability of the ONE architecture, which not only leverages the advantages of high-performance dual-space processing for outperforming traditional PDE solvers and being comparable with state-of-the-art ML models but also can be implemented using optical computing hardware with unique features of low-energy and highly parallel constant-time processing irrespective of model scales and real-time reconfigurability for tackling multiple tasks with the same architecture. The demonstrated architecture offers a versatile and powerful platform for large-scale scientific and engineering computations.