# Different Paths, Same Destination: Designing New Physics-Inspired Dynamical Systems with Engineered Stability to Minimize the Ising Hamiltonian

arXiv: https://arxiv.org/abs/2504.06280 · HTML: https://mlsanity.com/paper/2504.06280/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Builds on (most cited first, 6 of 6)

- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Computational Models based on Synchronized Oscillators for Solving Combinatorial Optimization Problems](https://mlsanity.com/paper/2206.05907/) (2022)
- [Dynamical system-based computational models for solving combinatorial optimization on hypergraphs](https://mlsanity.com/paper/2207.09618/) (2022)
- [Stability of Oscillator Ising Machines: Not All Solutions Are Created Equal](https://mlsanity.com/paper/2301.07601/) (2023)
- [A Note on Analyzing the Stability of Oscillator Ising Machines](https://mlsanity.com/paper/2310.09322/) (2023)
- [Collective dynamics of phase-repulsive oscillators solves graph coloring problem](https://mlsanity.com/paper/1909.06095/) (2019)

## Abstract (arXiv)

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.