arXiv:2604. 06531v3 Announce Type: replace-cross Abstract: The mean-field Schr\"odinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution from another by a fixed deadline.
By Asmaa Eldesoukey, Yongxin Chen, Abhishek Halder
The paper presents a new formulation of the Schr"odinger bridge problem on graphs that incorporates state costs via a Feynman‑Kac tilt, eliminating the need for learned control or temporal‑difference penalties. The resulting cost‑augmented bridge is solved exactly by alternating two endpoint rescalings, each requiring only a sparse matrix‑exponential application, and the method scales linearly with network size. Experiments on a protein‑folding model and a large road‑network demonstrate that the exact bridge reduces expected energy barriers and matches target distributions within sampling error.
By Akshay Balsubramani
The paper studies finite‑horizon minimum‑energy steering of inertial swarms under stochastic disturbances, focusing on mean‑field models with Cucker–Smale alignment or Morse attraction–repulsion interactions. It formulates the problem as a Schr"odinger bridge, deriving nonlinear, time‑symmetric optimality systems and proposing nested fixed‑point schemes for numerical solution. Numerical experiments demonstrate that the optimal corrective drift can either exploit or counteract the natural interaction forces, depending on their alignment with the steering objective.
By Asmaa Eldesoukey, Md Zulfiqur Haider, Italo Napolitano, Yongxin Chen, Abhishek Halder
The paper introduces a mesh‑free, self‑supervised neural operator—called the Normalizing Flow Invertible Solution Transformer (NFIST)—for stochastic mean‑field control (MFC). By reformulating the controlled Fokker–Planck dynamics as a deterministic continuity equation via a probability‑flow ODE and an invertible normalizing‑flow transformer, the authors enable closed‑form score evaluation with linear cost per particle. The resulting operator learns from task prompts (distribution parameters or particle clouds) and can solve unseen MFC tasks in a single forward pass, achieving zero‑shot generalization across applications such as stochastic optimal control, Schrödinger bridges, systemic‑risk control, and obstacle‑avoiding path planning.
By Suyi Gao, Mo Zhou, Rongjie Lai
arXiv:2606. 15871v1 Announce Type: cross Abstract: Bayesian inference for inverse problems is run to evaluate integrals -- posterior expectations, tail probabilities, and risks -- across a stream of observations.
By Ali Siahkoohi
arXiv:2605.29371v2 Announce Type: replace-cross
Abstract: We study the subclass of potential mean-field games in which the running interaction cost and the terminal target cost are both expressed thr...
By Yumiharu Nakano