用振荡神经网络模拟热力学机制求解矩阵逆，理论与仿真均验证其有效性。
Thermodynamics-Inspired Computing with Oscillatory Neural Networks for Inverse Matrix Computation
- 基于耦合基拉诺振子模型的线性近似，将热力学原理融入矩阵求逆计算。
- 数值模拟显示在特定参数区间内，计算精度可达95%以上。
- 适合对类脑计算、物理启发算法感兴趣的科研人员参考。
我们提出一种受热力学启发的计算范式，基于振荡神经网络（ONNs）求解线性代数问题中的矩阵逆。尽管ONNs已被广泛研究作为解决复杂组合优化问题的伊辛机，但本文首次探讨其在求解矩阵逆问题上的可行性。基于热力学原理，我们从理论上证明：耦合基拉诺振子模型的线性近似可导出矩阵逆的解。数值仿真验证了该理论框架的正确性，并分析了不同参数区间下的计算精度表现，结果表明在特定参数条件下，计算准确率可达95%以上。
原文摘要 · Abstract (English)
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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