Optical Neural Engine for Solving Scientific Partial Differential Equations

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 combin-

ing 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’s 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 tra-

ditional PDE solvers and being comparable with state-of-the-art ML models but

also can be implemented using optical computing hardware with unique fea-

tures 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