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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We extend the concept of self-consistency for the Fokker-Planck equation(FPE) to the more general McKean-Vlasov equation (MVE). While FPE describes themacroscopic behavior of particles under drift and diffusion, MVE accounts forthe additional inter-particle interactions, which are often highly singular inphysical systems. Two important examples considered in this paper are the MVEwith Coulomb interactions and the vorticity formulation of the 2D Navier-Stokesequation. We show that a generalized self-consistency potential controls theKL-divergence between a hypothesis solution to the ground truth, throughentropy dissipation. Built on this result, we propose to solve the MVEs byminimizing this potential function, while utilizing the neural networks forfunction approximation. We validate the empirical performance of our approachby comparing with state-of-the-art NN-based PDE solvers on several exampleproblems.

Entropy-dissipation Informed Neural Network for McKean-Vlasov Type PDEs