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

• URL: http://arxiv.org/abs/2507.22544v1
• Date: Wed, 30 Jul 2025 10:16:55 GMT
• Title: Thermodynamics-Inspired Computing with Oscillatory Neural Networks for Inverse Matrix Computation
• Authors: George Tsormpatzoglou, Filip Sabo, Aida Todri-Sanial,
• Abstract summary: ONNs have been widely studied as Ising machines for tackling complex optimization problems.<n>This work investigates their feasibility in solving linear algebra problems, specifically the inverse matrix.
• Score: 0.4887814315732678
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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