# Schr"odinger Meets Kuramoto via Feynman-Kac: Minimum Effort Distribution Steering for Noisy Nonuniform Kuramoto Oscillators

arXiv: https://arxiv.org/abs/2202.09734 · HTML: https://mlsanity.com/paper/2202.09734/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2022.

## Built on by (most cited first, 7 of 7)

- [Schr"odinger Bridge with Quadratic State Cost is Exactly Solvable](https://mlsanity.com/paper/2406.00503/) (2024)
- [Neural Schr"odinger Bridge with Sinkhorn Losses: Application to Data-driven Minimum Effort Control of Colloidal Self-assembly](https://mlsanity.com/paper/2307.14442/) (2023)
- [A Physics-informed Deep Learning Approach for Minimum Effort Stochastic Control of Colloidal Self-Assembly](https://mlsanity.com/paper/2208.09182/) (2022)
- [Solution of the Probabilistic Lambert Problem: Connections with Optimal Mass Transport, Schr"odinger Bridge and Reaction-Diffusion PDEs](https://mlsanity.com/paper/2401.07961/) (2024)
- [Stochastic Learning of Computational Resource Usage as Graph Structured Multimarginal Schr"odinger Bridge](https://mlsanity.com/paper/2405.12463/) (2024)
- [Optimal Mass Transport over the Euler Equation](https://mlsanity.com/paper/2304.00595/) (2023)
- [Schr"odinger Bridges over Kinetic Swarming Models](https://mlsanity.com/paper/2608.25281/) (2026)

## Abstract (arXiv)

We formulate and solve the problem of finite horizon minimum control effort steering of the state probability distribution between prescribed endpoint joints for a finite population of networked noisy nonuniform Kuramoto oscillators. We consider both the first and second order stochastic Kuramoto models. For numerical solution of the associated stochastic optimal control, we propose combining certain measure-valued proximal recursions and the Feynman-Kac path integral computation. We illustrate the proposed framework via numerical examples.