用不同动力学系统求解同一优化问题，提升计算稳定性。
Different Paths, Same Destination: Designing New Physics-Inspired Dynamical Systems with Engineered Stability to Minimize the Ising Hamiltonian
- 设计新动力学系统DIM，与振荡器伊辛机同目标但动态特性不同。
- 不同图结构下模型表现各异，组合使用可降低对输入图的敏感性。
- 适合研究物理启发式优化方法、需鲁棒解的复杂组合问题求解者。
振荡器伊辛机（OIM）是利用物理启发的非线性动力系统求解计算难题——组合优化问题（COP）的典型代表。此类系统的计算性能高度依赖于底层动力学特性、输入图拓扑及其相互兼容性。本文探索了设计多种最小化同一目标函数但具有显著不同动力学特性的系统。目标是通过动力学多样性降低计算性能对输入图的敏感性，从而提升基于物理的计算方法的整体有效性。为此，我们提出一种新型动力系统——动力学伊辛机（DIM），其与OIM一样最小化伊辛哈密顿量，但具有截然不同的动力学特性。我们分析了DIM的特征并将其与OIM进行对比。结果表明，各模型的相对性能取决于输入图。本工作说明：使用多种动力学特性各异的系统求解同一组合优化问题，是一种对输入图不敏感且能产生鲁棒解的有效方法。
原文摘要 · Abstract (English)
Oscillator Ising machines (OIMs) represent an exemplar case of using physics-inspired non-linear dynamical systems to solve computationally challenging combinatorial optimization problems (COPs). The computational performance of such systems is highly sensitive to the underlying dynamical properties, the topology of the input graph, and their relative compatibility. In this work, we explore the concept of designing different dynamical systems that minimize the same objective function but exhibit drastically different dynamical properties. Our goal is to leverage this diversification in dynamics to reduce the sensitivity of the computational performance to the underlying graph, and subsequently, enhance the overall effectiveness of such physics-based computational methods. To this end, we introduce a novel dynamical system, the Dynamical Ising Machine (DIM), which, like the OIM, minimizes the Ising Hamiltonian but offers significantly different dynamical properties. We analyze the characteristic properties of the DIM and compare them with those of the OIM. We also show that the relative performance of each model is dependent on the input graph. Our work illustrates that using multiple dynamical systems with varying properties to solve the same COP enables an effective method that is less sensitive to the input graph, while producing robust solutions.
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