# Solving Sparse Finite Element Problems on Neuromorphic Hardware

arXiv: https://arxiv.org/abs/2501.10526 · HTML: https://mlsanity.com/paper/2501.10526/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 50 references that are in the map.
- First posted on arXiv 17 Jan 2025.

## Builds on (most cited first, 8 of 8)

- [The Hardware Lottery](https://mlsanity.com/paper/2009.06489/) (2020)
- [Physics-Informed Deep Neural Operator Networks](https://mlsanity.com/paper/2207.05748/) (2022)
- [Efficient Neuromorphic Signal Processing with Loihi 2](https://mlsanity.com/paper/2111.03746/) (2021)
- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [Can Physics-Informed Neural Networks beat the Finite Element Method?](https://mlsanity.com/paper/2302.04107/) (2023)
- [Efficient Video and Audio processing with Loihi 2](https://mlsanity.com/paper/2310.03251/) (2023)
- [Neuromorphic scaling advantages for energy-efficient random walk computation](https://mlsanity.com/paper/2107.13057/) (2021)
- [Stochastic Rounding 2.0, with a View towards Complexity Analysis](https://mlsanity.com/paper/2410.10517/) (2024)

## Built on by (most cited first, 8 of 8)

- [Intrinsic Numerical Robustness and Fault Tolerance in a Neuromorphic Algorithm for Scientific Computing](https://mlsanity.com/paper/2603.10246/) (2026)
- [The role of neuromorphic principles in the future of biomedicine and healthcare](https://mlsanity.com/paper/2603.27716/) (2026)
- [SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving](https://mlsanity.com/paper/2604.11625/) (2026)
- [NeuroAI and Beyond: Bridging Between Advances in Neuroscience and Artificial Intelligence](https://mlsanity.com/paper/2604.18637/) (2026)
- [Event-driven Robust Fitting on Neuromorphic Hardware](https://mlsanity.com/paper/2508.09466/) (2025)
- [Gradient-Free Continual Learning in Spiking Neural Networks via Inter-Spike Interval Regularization](https://mlsanity.com/paper/2604.16496/) (2026)
- [Robust PnP on a Neuromorphic Processor for Object Pose Estimation](https://mlsanity.com/paper/2607.16834/) (2026)
- [Neuromorphic Object Detection: An In-Depth Study and Future Directions](https://mlsanity.com/paper/2607.23576/) (2026)

## Abstract (arXiv)

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.