# Thermodynamics-Inspired Computing with Oscillatory Neural Networks for Inverse Matrix Computation

arXiv: https://arxiv.org/abs/2507.22544 · HTML: https://mlsanity.com/paper/2507.22544/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 30 Jul 2025.

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

- [An Introduction to Convolutional Neural Networks](https://mlsanity.com/paper/1511.08458/) (2015)
- [Thermodynamic Computing System for AI Applications](https://mlsanity.com/paper/2312.04836/) (2023)
- [Thermodynamic AI and the fluctuation frontier](https://mlsanity.com/paper/2302.06584/) (2023)
- [Thermodynamic Computing](https://mlsanity.com/paper/1911.01968/) (2019)
- [A full-stack view of probabilistic computing with p-bits: devices, architectures and algorithms](https://mlsanity.com/paper/2302.06457/) (2023)
- [Efficient Optimization with Higher-Order Ising Machines](https://mlsanity.com/paper/2212.03426/) (2022)
- [Thermodynamic Neural Network](https://mlsanity.com/paper/1906.01678/) (2019)
- [Increasing the clock speed of a thermodynamic computer by adding noise](https://mlsanity.com/paper/2410.12211/) (2024)

## Abstract (arXiv)

We describe a thermodynamic-inspired computing paradigm based on oscillatory neural networks (ONNs). While ONNs have been widely studied as Ising machines for tackling complex combinatorial optimization problems, this work investigates their feasibility in solving linear algebra problems, specifically the inverse matrix. Grounded in thermodynamic principles, we analytically demonstrate that the linear approximation of the coupled Kuramoto oscillator model leads to the inverse matrix solution. Numerical simulations validate the theoretical framework, and we examine the parameter regimes that computation has the highest accuracy.