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

Neural networks (NNs) that exploit strong inductive biases based on physicallaws and symmetries have shown remarkable success in learning the dynamics ofphysical systems directly from their trajectory. However, these works focusonly on the systems that follow deterministic dynamics, for instance, Newtonianor Hamiltonian dynamics. Here, we propose a framework, namely Brownian graphneural networks (BROGNET), combining stochastic differential equations (SDEs)and GNNs to learn Brownian dynamics directly from the trajectory. Wetheoretically show that BROGNET conserves the linear momentum of the system,which in turn, provides superior performance on learning dynamics as revealedempirically. We demonstrate this approach on several systems, namely, linearspring, linear spring with binary particle types, and non-linear springsystems, all following Brownian dynamics at finite temperatures. We show thatBROGNET significantly outperforms proposed baselines across all the benchmarkedBrownian systems. In addition, we demonstrate zero-shot generalizability ofBROGNET to simulate unseen system sizes that are two orders of magnitude largerand to different temperatures than those used during training. Altogether, ourstudy contributes to advancing the understanding of the intricate dynamics ofBrownian motion and demonstrates the effectiveness of graph neural networks inmodeling such complex systems.

Graph Neural Stochastic Differential Equations for Learning Brownian Dynamics