Capabilities and Limitations of Time-lagged Autoencoders for Slow Mode Discovery in Dynamical Systems

Abstract

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.

References in corpus (11)

• Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
• Identification of slow molecular order parameters for Markov model construction
• VAMPnets: Deep learning of molecular kinetics
• Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
• On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator
• Data-driven model reduction and transfer operator approximation
• Variational Encoding of Complex Dynamics
• Nonlinear Discovery of Slow Molecular Modes using State-Free Reversible VAMPnets
• Stochastic thermostats: comparison of local and global schemes
• On the correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations
• Note: Variational Encoding of Protein Dynamics Benefits from Maximizing Latent Autocorrelation

Cited by in corpus (10)

• A unified framework for machine learning collective variables for enhanced sampling simulations: $\text{mlcolvar}$
• Deep Learning Collective Variables from Transition Path Ensemble
• Enhanced Sampling in the Age of Machine Learning: Algorithms and Applications
• A Deep Autoencoder Framework for Discovery of Metastable Ensembles in Biomacromolecules
• Recent advances in describing and driving crystal nucleation using machine learning and artificial intelligence
• PySAGES: flexible, advanced sampling methods accelerated with GPUs
• Understanding the role of predictive time delay and biased propagator in RAVE
• A Functional approach for Two Way Dimension Reduction in Time Series
• Identifying the leading dynamics of ubiquitin: a comparison between the tICA and the LE4PD slow fluctuations in amino acids' position
• Variational embedding of protein folding simulations using gaussian mixture variational autoencoders