Solving Sparse Finite Element Problems on Neuromorphic Hardware
This enables energy-efficient and parallel solutions for engineering and scientific problems using neuromorphic hardware, representing an incremental advance in hardware-specific applications.
The authors tackled the problem of implementing the finite element method on neuromorphic hardware to leverage its energy efficiency and parallelism, achieving comparable numerical accuracy and scaling for the Poisson equation on the Intel Loihi 2 platform.
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.