Repository: Freie Universität Berlin, Math Department

Analyzing multimodal probability measures with autoencoders

Lelièvre, Tony and Pigeon, Thomas and Stoltz, Gabriel and Zhang, Wei (2023) Analyzing multimodal probability measures with autoencoders. To appear in The Journal of Physical Chemistry B . (In Press)

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Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively used to complement and possibly bypass expert knowledge in order to construct collective variables. Our focus here is on neural network approaches based on autoencoders. We study some relevant mathematical properties of the loss function considered for training autoencoders, and provide physical interpretations based on conditional variances and minimum energy paths. We also consider various extensions in order to better describe physical systems, by incorporating more information on transition states at saddle points, and/or allowing for multiple decoders in order to describe several transition paths. Our results are illustrated on toy two dimensional systems and on alanine dipeptide.

Item Type:Article
Subjects:Mathematical and Computer Sciences
Mathematical and Computer Sciences > Mathematics
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:3128
Deposited By: Lukas-Maximilian Jaeger
Deposited On:26 Feb 2024 12:01
Last Modified:26 Feb 2024 12:01

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