Solving sparse finite element problems on neuromorphic hardware

Theilman, Bradley Harold; Aimone, James Bradley

doi:10.1038/s42256-025-01143-2

Solving sparse finite element problems on neuromorphic hardware

Journal Article · Thu Nov 13 00:00:00 EST 2025 · Nature Machine Intelligence

DOI:https://doi.org/10.1038/s42256-025-01143-2· OSTI ID:3006560

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Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

The finite element method (FEM) is one of the most important and ubiquitous numerical methods for solving partial differential equations (PDEs) on computers for scientific and engineering discovery. Applying the FEM to larger and more detailed scientific models has driven advances in high-performance computing for decades. Here we demonstrate that scalable spiking neuromorphic hardware can directly implement the FEM by constructing a spiking neural network that solves the large, sparse, linear systems of equations at the core of the FEM. We show that for the Poisson equation, a fundamental PDE in science and engineering, our neural circuit achieves meaningful levels of numerical accuracy and close to ideal scaling on modern, inherently parallel and energy-efficient neuromorphic hardware, specifically Intel’s Loihi 2 neuromorphic platform. We illustrate extensions to irregular mesh geometries in both two and three dimensions as well as other PDEs such as linear elasticity. Our spiking neural network is constructed from a recurrent network model of the brain’s motor cortex and, in contrast to black-box deep artificial neural network-based methods for PDEs, directly translates the well-understood and trusted mathematics of the FEM to a natively spiking neuromorphic algorithm.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: NA0003525

OSTI ID:: 3006560

Report Number(s):: SAND--2025-14922J; 1762119

Journal Information:: Nature Machine Intelligence, Journal Name: Nature Machine Intelligence Journal Issue: 11 Vol. 7; ISSN 2522-5839

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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