# Schr"odinger Bridges over Kinetic Swarming Models

arXiv: https://arxiv.org/abs/2608.25281 · HTML: https://mlsanity.com/paper/2608.25281/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 98 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Builds on (most cited first, 23 of 23)

- [On the relation between optimal transport and Schr"odinger bridges: A stochastic control viewpoint](https://mlsanity.com/paper/1412.4430/) (2014)
- [Wasserstein Proximal Algorithms for the Schr"odinger Bridge Problem: Density Control with Nonlinear Drift](https://mlsanity.com/paper/1912.01244/) (2019)
- [Trajectory Inference via Mean-field Langevin in Path Space](https://mlsanity.com/paper/2205.07146/) (2022)
- [Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems](https://mlsanity.com/paper/2010.03729/) (2020)
- [The most likely evolution of diffusing and vanishing particles: Schrodinger Bridges with unbalanced marginals](https://mlsanity.com/paper/2108.02879/) (2021)
- [Density control of interacting agent systems](https://mlsanity.com/paper/2108.07342/) (2021)
- [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)
- [Collective behavior from surprise minimization](https://mlsanity.com/paper/2307.14804/) (2023)
- [A Physics-informed Deep Learning Approach for Minimum Effort Stochastic Control of Colloidal Self-Assembly](https://mlsanity.com/paper/2208.09182/) (2022)
- [Schr"odinger Meets Kuramoto via Feynman-Kac: Minimum Effort Distribution Steering for Noisy Nonuniform Kuramoto Oscillators](https://mlsanity.com/paper/2202.09734/) (2022)
- [Control to flocking of the kinetic Cucker-Smale model](https://mlsanity.com/paper/1411.4687/) (2014)
- [Optimal consensus control of the Cucker-Smale model](https://mlsanity.com/paper/1802.01529/) (2018)
- [Propagation of chaos for mean field Schr"odinger problems](https://mlsanity.com/paper/2304.09340/) (2023)
- [On the Hopf-Cole Transform for Control-affine Schr"odinger Bridge](https://mlsanity.com/paper/2503.17640/) (2025)
- [Continuification-based control of large multiagent systems in a ring](https://mlsanity.com/paper/2209.15060/) (2022)
- [Schr"odinger's control and estimation paradigm with spatio-temporal distributions on graphs](https://mlsanity.com/paper/2312.05679/) (2023)
- [Fast cooling for a system of stochastic oscillators](https://mlsanity.com/paper/1411.1323/) (2014)
- [A Generalized Sinkhorn Algorithm for Mean-Field Schr"odinger Bridge](https://mlsanity.com/paper/2604.06531/) (2026)
- [A Controlled Mean Field Model for Chiplet Population Dynamics](https://mlsanity.com/paper/2303.10564/) (2023)
- [Hierarchical Learning-Based Control for Multi-Agent Shepherding of Stochastic Autonomous Agents](https://mlsanity.com/paper/2508.02632/) (2025)
- [Bio-inspired density control of multi-agent swarms via leader-follower plasticity](https://mlsanity.com/paper/2507.15781/) (2025)
- [Sparse shepherding control of large-scale multi-agent systems via Reinforcement Learning](https://mlsanity.com/paper/2511.21304/) (2025)
- [Nonlocal Mean Field Schr"odinger Bridge with Learned Interactions](https://mlsanity.com/paper/2606.04265/) (2026)

## Abstract (arXiv)

Paradigmatic interaction models explain how collective behaviors can emerge in complex systems from interactions among the constituent agents. In bio-inspired swarms, however, interactions alone may not suffice to bring the population to a desired aggregate configuration within a prescribed time horizon, as needed in applications ranging from targeted therapy to collective transport and emergency evacuation. In the present work, we consider finite-horizon minimum-energy collective steering for inertial swarms that are subject to stochastic disturbances. We focus on the mean-field representations of these multi-agent systems driven by Cucker--Smale alignment or Morse attraction--repulsion interactions. Our objective is to steer the swarm between prescribed endpoint distributions using a state-feedback control, where the endpoint specifications can be full phase-space distributions (positions and velocities) or position marginals alone. Our formalism is rooted in the theory of Schr"odinger bridges, which has inspired contemporary developments spanning statistical inference, biological modeling, stochastic control, and generative learning. Within the bridges framework, the uncontrolled interacting stochastic dynamics are viewed as a prior model, and the optimal control as the minimum-energy corrective drift needed to realize the prescribed distributions. We derive nonlinear, coupled necessary optimality systems with a time-symmetric structure reminiscent of classical Schr"odinger bridges, and propose nested fixed-point schemes to numerically solve them. Numerical examples show that the obtained optimal control (corrective drift) can dynamically exploit or counteract the interaction forces, depending on whether the latter are favorable or adversarial to the steering task.