Analog Photonic Computing Engine as Approximate Partial Differential Equation Solver

The class of partial differential equations are ubiquitous to a plurality of fields including science, engineering, economics and medicine, and require time-iterative algorithms when solved with digital processors. In contrast, analog electronic compute engines have demonstrated to outperform digital systems for special-purpose processing due to their non-iterative operation nature. However, their electronic circuitry sets fundamental challenges in terms of run-time and programmability-speed. Integrated photonic circuits, however, enables both analog compute-hardware while exploiting time parallelism known from optics, while leveraging wafer-scale dense integration. Here, we introduce a photonic partial differential equation solver based on a Manhattan mesh-grid network featuring symmetrical power splitters and arbitrary Dirichlet boundary conditions. Our design numerically and experimentally solves a second-order elliptic partial differential equation with over 97% accuracy against solutions computed through commercially available solvers, achieving a steady state solution in 16 ps and providing a pathway towards real-time, chip-scale, reconfigurable application-specific photonic integrated circuits (ASPICs).