English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We present a novel computational framework for density control inhigh-dimensional state spaces. The considered dynamical system consists of alarge number of indistinguishable agents whose behaviors can be collectivelymodeled as a time-evolving probability distribution. The goal is to steer theagents from an initial distribution to reach (or approximate) a given targetdistribution within a fixed time horizon at minimum cost. To tackle thisproblem, we propose to model the drift as a nonlinear reduced-order model, suchas a deep network, and enforce the matching to the target distribution atterminal time either strictly or approximately using the Wasserstein metric.The resulting saddle-point problem can be solved by an effective numericalalgorithm that leverages the excellent representation power of deep networksand fast automatic differentiation for this challenging high-dimensionalcontrol problem. A variety of numerical experiments were conducted todemonstrate the performance of our method.

High-dimensional Optimal Density Control with Wasserstein Metric Matching