DIODES: Diffractive Optical Differential Equation Solver

ABSTRACT

Efficient partial differential equation (PDE) solving is central to scientific and engineering applications, and data‐driven approaches have emerged as fast alternatives for large‐scale problems. However, their deployment remains dominated by electronic hardware with growing energy and integration density constraints. Optical and photonic computing offers a high‐throughput and energy‐efficient platform, but existing optical PDE solvers remain limited by hardware complexity and scalability. Here, we present a diffractive optical differential equation solver (DIODES) architecture that combines real‐space and Fourier‐space optical processing in a streamlined hardware implementation built mainly from diffractive components. DIODES removes optical matrix–vector multiplier hardware and enables nonlinear optical processing using linear optics instead of electronic nonlinear modules, providing a practical route toward all‐optical PDE solvers. We demonstrate DIODES on the time‐independent Darcy flow equation, achieving strong predictive capability, resolution‐scalable trainability, and performance comparable to representative optical and electronic models. To guide experimental implementation, we also analyze various experimental nonidealities and show that experiment‐aware training improves robustness to static nonidealities. Finally, we extend DIODES to time‐dependent Maxwell's equations in a dielectric metasurface example. These results establish DIODES as a streamlined optical computing framework for scalable, high‐throughput, and energy‐efficient PDE solving.