🤖 AI Summary
Solving large-scale sparse linear systems in high-performance computing faces significant challenges due to high latency and energy consumption. This work proposes a novel optical analog computing paradigm by, for the first time, mapping general sparse linear systems onto the phase dynamics of coupled laser cavities within an optical Laser Processing Unit (LPU), where the steady-state optical field directly encodes the solution. By integrating laser cavity modeling with LPU simulation, the method demonstrates superior performance over GPU-based Krylov subspace solvers—such as Conjugate Gradient (CG) and GMRES—on standard SuiteSparse multi-band sparse matrices, achieving substantially lower solution latency, higher parallelism, and improved energy efficiency.
📝 Abstract
Solving large, sparse linear systems is a fundamental workload in scientific computing and engineering simulations, often dominating runtime and energy consumption in high-performance computing (HPC) applications. In this work, we explore an alternative computing paradigm based on analog optical processing, implemented through the Laser Processing Unit (LPU). The LPU encodes linear systems into the dynamics of coupled lasers within an optical cavity, where the steady-state phases of the optical fields correspond to the solution of $Ax=b$. We present a mapping of general linear systems, both dense and sparse, onto the LPU architecture and evaluate its performance using representative matrices from the SuiteSparse collection. Using an LPU emulator, we benchmark convergence behavior and time-to-solution for sparse, multi-banded matrices against established Krylov subspace methods (CG, GMRES, BiCGSTAB, and others) executed on a modern GPU platform. Our results demonstrate that the LPU will achieve significantly lower time-to-solution for selected problem classes, highlighting the potential of optical analog computing for accelerating iterative linear solvers. These findings suggest that optical processors such as the LPU will be able to serve as accelerators for linear systems, in particular structured and/or repeatedly solved, offering advantages in latency, parallelism, and energy efficiency. We discuss current limitations, including scaling constraints and precision considerations, and outline directions toward hybrid optical-digital computing systems.