基于振荡神经网络的图着色方法求解数独
Graph Coloring Approach to Solving Sudoku with Oscillatory Neural Networks
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中文总结 AI 辅助
研究提出用振荡神经网络求解数独，将其转化为图着色问题，通过修改求解器并引入附加项，在准确性上优于现有求解器，在4×4和9×9数独上分别有近乎完美及较高准确率。
中文摘要 AI 辅助
振荡神经网络（ONNs）是一种基于物理学的计算范式，源于典型的全耦合振荡器网络动力学，旨在最小化潜在能量函数。本文提出一种基于ONN的数独求解器，将数独问题转化为图着色问题。通过将现有的图着色求解器修改为计算成本更低的版本，并引入确保数独约束满足的附加项，该求解器在准确性方面显著优于现有的HNN和ONN求解器。特别是，对于不同数量的未知数字，在4×4数独上能实现近乎完美的准确率，在9×9数独上也有较高准确率。
英文摘要
Oscillatory Neural Networks (ONNs) present an attractive physics-based computing paradigm rooted in the dynamics of a network of typically fully coupled oscillators aiming to minimize an underlying energy function. In this paper, we propose an ONN-based solver for one well-known constrained combinatorial optimization problem, namely a Sudoku, by formulating the problem as a Graph Coloring problem. By modifying the already existing Graph Coloring solver to a computationally cheaper version and introducing an additional term ensuring the fulfillment of the Sudoku constraints, our solver is shown to significantly outperform the existing HNN- and ONN solvers in terms of accuracy. In particular, we are able to achieve nearly flawless accuracies on $4 \times 4$ as well as rather high accuracies on $9 \times 9$ Sudoku puzzles for different numbers of unknown digits.
