Capabilities and Limitations of Time-lagged Autoencoders for Slow Mode Discovery in Dynamical Systems
This work addresses the limitations of TAEs for researchers in computational chemistry and physics, providing incremental insights by comparing them with SRVs.
The paper rigorously analyzes time-lagged autoencoders (TAEs) for discovering slow modes in dynamical systems, showing they often learn a mix of slow and maximum variance modes, and demonstrates that state-free reversible VAMPnets (SRVs) outperform TAEs in correctly identifying slow modes in specific examples like the alanine dipeptide molecule.
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 VAMPnets (SRVs) as a variational-based neural network approach for slow modes discovery, and show that SRVs can correctly discover slow modes where TAEs fail.