aiqbench analysis
This paper uses a shared neural network to replace the repeated forward-backward PDE solves that make mean-field planners slow for online replanning, trading an offline training step for cheap, fixed-coefficient control at runtime. The reported gains are accuracy-runtime trade-offs and lower transport error than classical feedback baselines, so the value depends on how the method scales beyond the periodic-domain model with its error bounds. Readers interested in learned surrogates for control PDEs should check the training cost and the boundary-flux penalty's effect on results.
Rapid Mean-Field Formation Transport with a Shared-Representation Neural Fokker-Planck Controller
arXiv:2611.03981v1 Announce Type: new Abstract: This paper develops a mean-field formation transport method with low online computational cost for large-scale multi-agent systems. Classical mean-field planners often require repeated solutions of coupled forward and backward partial differential equations, making online replanning computationally demanding. Density and control are therefore approximated by a common parameterized nonlinear map with separate scalar density and vector control outputs. Parameters are optimized using Fokker--Planck and initial-condition residuals, formation-matching costs on numerically simulated closed-loop particle trajectories, and control effort. Numerical computations are restricted to a bounded region of the state space, with an additional penalty on probability flux across its boundary. For the periodic-domain model, we establish well-posedness of the induced density evolution and bound the density-approximation error in terms of the dynamics and initial-condition residuals. Parameter optimization precedes online operation, during which controller coefficients remain fixed. Experiments quantify the accuracy--runtime trade-off relative to a mean-field planner, show lower transport error than classical feedback baselines, and demonstrate the benefits of the common parameterization.
Abstract:This paper develops a mean-field formation transport method with low online computational cost for large-scale multi-agent systems. Classical mean-field planners often require repeated solutions of coupled forward and backward partial differential equations, making online replanning computationally demanding. Density and control are therefore approximated by a common parameterized nonlinear map with separate scalar density and vector control outputs. Parameters are optimized using Fokker--Planck and initial-condition residuals, formation-matching costs on numerically simulated closed-loop particle trajectories, and control effort. Numerical computations are restricted to a bounded region of the state space, with an additional penalty on probability flux across its boundary. For the periodic-domain model, we establish well-posedness of the induced density evolution and bound the density-approximation error in terms of the dynamics and initial-condition residuals. Parameter optimization precedes online operation, during which controller coefficients remain fixed. Experiments quantify the accuracy--runtime trade-off relative to a mean-field planner, show lower transport error than classical feedback baselines, and demonstrate the benefits of the common parameterization.
Machine Learning (cs.LG)
arXiv:2611.03981 [cs.LG]
(or arXiv:2611.03981v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2611.03981 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 254 words