Solving Sparse Finite Element Problems on Neuromorphic Hardware

Fuente: arXiv
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Main Authors: Theilman, Bradley H., Aimone, James B.
Format: Preprint
Published: 2025
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author Theilman, Bradley H.
Aimone, James B.
author_facet Theilman, Bradley H.
Aimone, James B.
contents We demonstrate that scalable neuromorphic hardware can implement the finite element method, which is a critical numerical method for engineering and scientific discovery. Our approach maps the sparse interactions between neighboring finite elements to small populations of neurons that dynamically update according to the governing physics of a desired problem description. We show that for the Poisson equation, which describes many physical systems such as gravitational and electrostatic fields, this cortical-inspired neural circuit can achieve comparable levels of numerical accuracy and scaling while enabling the use of inherently parallel and energy-efficient neuromorphic hardware. We demonstrate that this approach can be used on the Intel Loihi 2 platform and illustrate how this approach can be extended to nontrivial mesh geometries and dynamics.
format Preprint
id arxiv_https___arxiv_org_abs_2501_10526
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Solving Sparse Finite Element Problems on Neuromorphic Hardware
Theilman, Bradley H.
Aimone, James B.
Neural and Evolutionary Computing
Artificial Intelligence
Machine Learning
Numerical Analysis
We demonstrate that scalable neuromorphic hardware can implement the finite element method, which is a critical numerical method for engineering and scientific discovery. Our approach maps the sparse interactions between neighboring finite elements to small populations of neurons that dynamically update according to the governing physics of a desired problem description. We show that for the Poisson equation, which describes many physical systems such as gravitational and electrostatic fields, this cortical-inspired neural circuit can achieve comparable levels of numerical accuracy and scaling while enabling the use of inherently parallel and energy-efficient neuromorphic hardware. We demonstrate that this approach can be used on the Intel Loihi 2 platform and illustrate how this approach can be extended to nontrivial mesh geometries and dynamics.
title Solving Sparse Finite Element Problems on Neuromorphic Hardware
topic Neural and Evolutionary Computing
Artificial Intelligence
Machine Learning
Numerical Analysis
url https://arxiv.org/abs/2501.10526