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.
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.
arXiv:2604. 08580v2 Announce Type: replace-cross Abstract: Reward fine-tuning of diffusion and flow models and sampling from tilted or Boltzmann distributions can both be formulated as stochastic optimal control (SOC) problems, where learning an optimal generative dynamics corresponds to optimizing a control under SDE constraints.
The paper presents a variational learning framework that simultaneously infers non‑parametric interaction kernels and environmental or intra‑agent forces in collective dynamics. It extends existing methods to handle both interaction and environmental components, validating the approach on benchmark models such as synchronization, alignment, and attraction‑repulsion systems. A model‑selection procedure is also introduced to identify the best explanatory framework from trajectory data, enabling direct recovery of mechanistic interaction mechanisms.
arXiv:2606. 04265v1 Announce Type: cross Abstract: The Schr\"odinger Bridge Problem constructs a stochastic process that connects an initial distribution to a terminal distribution with minimum energy.
arXiv:2607. 11005v1 Announce Type: cross Abstract: This paper develops a model-free reinforcement learning framework for continuous--time extended mean field control problems, where both the dynamics and reward may depend on the joint distribution of states and controls.
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.
arXiv:2604. 13213v2 Announce Type: replace-cross Abstract: Rare events such as conformational changes in biomolecules, phase transitions, and chemical reactions are central to the behavior of many physical systems, yet they are extremely difficult to study computationally because unbiased simulations seldom produce them.
The paper introduces a Physics‑Informed Multi‑Agent Coordination framework that embeds calibrated BCMP queueing topologies into a decentralized multi‑agent reinforcement learning system for hospital patient flow. It formulates the problem as a Decentralized Partially Observable Markov Decision Process with coupled resource constraints, enabling departmental agents to negotiate patient routing and service scaling while exchanging localized action fingerprints to handle non‑stationarity. Empirical tests on MIMIC‑IV data show the approach reduces cumulative system delay compared to static Markovian models, heuristic dispatching, and independent multi‑agent baselines, all while preserving clinical safety constraints.
arXiv:2509.26364v3 Announce Type: replace Abstract: The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certa...
arXiv:2609.13758v1 Announce Type: cross Abstract: We establish the equivalence between the stochastic optimal control and path space formulations of the Schr\"odinger bridge problem (SBP) for the kin...
This paper addresses model-free continuous-time mean-field control in a setting where the population dynamics evolve continuously according to an unknown McKean-Vlasov stochastic differential equation, while only discrete-time transition data are available. In the model-based formulation, policy evaluation is naturally described by a stationary Hamilton-Jacobi-Bellman equation on $\mathcal P_2(\mathbb R^d)$, but this equation involves the drift and diffusion coefficients of the controlled McKean-Vlasov dynamics, which are not identifiable when only discrete-time data are available.
arXiv:2509. 23960v2 Announce Type: replace-cross Abstract: Co-optimizing safety and performance in large-scale multi-agent systems remains a fundamental challenge.