Solving Sparse Finite Element Problems on Neuromorphic Hardware

TL;DR

This paper demonstrates that neuromorphic hardware can efficiently implement the finite element method for solving PDEs like the Poisson equation, achieving accuracy and scalability with energy efficiency.

Contribution

It introduces a neural circuit mapping finite element interactions onto neuromorphic hardware, enabling scalable and energy-efficient PDE solutions.

Findings

Achieves comparable accuracy to traditional methods

Demonstrates scalability on Intel Loihi 2 platform

Extends to complex mesh geometries and dynamics

Abstract

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.