Integrated photonic multigrid solver for partial differential equations

TL;DR

This paper introduces a photonic multigrid solver that significantly accelerates partial differential equation solutions by offloading smoothening to optical hardware, achieving over 80% reduction in digital operations and up to 97% in specific simulations.

Contribution

It presents a novel mixed-precision photonic multigrid solver that integrates optical and digital processing for efficient PDE solving, demonstrating substantial speedups.

Findings

Reduces digital operations by over 80% in PDE solving.

Achieves up to 97% digital operation reduction in LQCD calculations.

Enables an order-of-magnitude increase in computational speed.

Abstract

Solving partial differential equations is crucial to analysing and predicting complex, large-scale physical systems but pushes conventional high-performance computers to their limits. Application specific photonic processors are an exciting computing paradigm for building efficient, ultrafast hardware accelerators. Here, we investigate the synergy between multigrid based partial differential equations solvers and low latency photonic matrix vector multipliers. We propose a mixed-precision photonic multigrid solver, that offloads the computationally demanding smoothening procedure to the optical domain. We test our approach on an integrated photonic accelerator operating at 2 GSPS solving a Poisson and Schr\"odinger equation. By offloading the smoothening operation to the photonic system, we can reduce the digital operation by more than 80%. Finally, we show that the photonic multigrid solver potentially reduces digital operations by up to 97 % in lattice quantum chromodynamics (LQCD) calculations, enabling an order-of-magnitude gain in computational speed and efficiency.