This repository explores how networks of coupled oscillators can be analog solvers of NP-Hard combinatorial optimization problems. The Kuramoto model describes the synchronization of coupled oscillators, and can be used to minimize Ising Hamiltonians, enabling physical systems to solve problems like MaxCut.
I lead the development of a custom circuit board (arXiv:2512.23720) as an experimental testbed for this oscillator-based computing framework.
The basic Kuramoto model can be extended to a stochastic differential equation with an added term to enforce binary phase configurations (Wang & Roychowdhury).
Figure: Solving a 100-node MaxCut instance with random Gaussian weights.
- Top: Oscillator phases evolving over time, eventually clustering near integer multiples of π that represent 0 or 1
- Second: Cut value compared to the optimal solution (gray line) found by a classical Tabu solver
- Third: Lyapunov energy decreasing as the system finds better configurations
- Bottom: Time-varying control annealing parameters
- Wang & Roychowdhury, OIM: Oscillator-based Ising Machines
- Chou et al., Analog Coupled Oscillator Based Weighted Ising Machine
- Hoppensteadt & Izhikevich, Oscillatory Neurocomputers with Dynamic Connectivity