Journal
JOURNAL OF CHEMICAL PHYSICS
Volume 151, Issue 6, Pages -Publisher
AIP Publishing
DOI: 10.1063/1.5112048
Keywords
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Funding
- National Science Foundation [CHE-1841805]
- Molecular Software Sciences Institute (MolSSI) Software Fellows program (NSF) [ACI-1547580]
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Time-lagged autoencoders (TAEs) have been proposed as a deep learning regression-based approach to the discovery of slow modes in dynamical systems. However, a rigorous analysis of nonlinear TAEs remains lacking. In this work, we discuss the capabilities and limitations of TAEs through both theoretical and numerical analyses. Theoretically, we derive bounds for nonlinear TAE performance in slow mode discovery and show that in general TAEs learn a mixture of slow and maximum variance modes. Numerically, we illustrate cases where TAEs can and cannot correctly identify the leading slowest mode in two example systems: a 2D Washington beltway potential and the alanine dipeptide molecule in explicit water. We also compare the TAE results with those obtained using state-free reversible variational approach for Markov processes nets (SRVs) as a variational-based neural network approach for slow mode discovery and show that SRVs can correctly discover slow modes where TAEs fail. Published under license by AIP Publishing.
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