Devergne, Timothée; Kostic, Vladimir R; Parrinello, Michele; Pontil, Massimiliano; (2024) From Biased to Unbiased Dynamics: An Infinitesimal Generator Approach. In: Globerson, A and Mackey, L and Belgrave, D and Fan, A and Paquet, U and Tomczak, J and Zhang, C, (eds.) Advances in Neural Information Processing Systems 37 (NeurIPS 2024). (pp. pp. 1-27). NeurIPS: Vancouver, BC, Canada.

Preview

Text NeurIPS-2024-from-biased-to-unbiased-dynamics-an-infinitesimal-generator-approach-Paper-Conference.pdf - Published Version Download (5MB) | Preview

Abstract

We investigate learning the eigenfunctions of evolution operators for time-reversal invariant stochastic processes, a prime example being the Langevin equation used in molecular dynamics. Many physical or chemical processes described by this equation involve transitions between metastable states separated by high potential barriers that can hardly be crossed during a simulation. To overcome this bottleneck, data are collected via biased simulations that explore the state space more rapidly. We propose a framework for learning from biased simulations rooted in the infinitesimal generator of the process {and the associated resolvent operator}. We contrast our approach to more common ones based on the transfer operator, showing that it can provably learn the spectral properties of the unbiased system from biased data. In experiments, we highlight the advantages of our method over transfer operator approaches and recent developments based on generator learning, demonstrating its effectiveness in estimating eigenfunctions and eigenvalues. Importantly, we show that even with datasets containing only a few relevant transitions due to sub-optimal biasing, our approachrecovers relevant information about the transition mechanism.

Download activity - last month

Export as JSONCSVXML

Download activity - last 12 months

Export as JSONXMLCSV

Downloads by country - last 12 months

Export as CSVXMLJSON

Archive Staff Only

View Item