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Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics

arXiv 1710.11239 ↗First posted 30 Oct 2017stat.ML cs.LG physics.bio-phcited by 64

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Abstract (arXiv)

Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for high-dimensional feature spaces which capture the slow dynamics of the underlying stochastic processes - beyond the capabilities of linear dimension reduction techniques.

Key facts. Cited by 64 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Oct 2017.

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Citing papers per year: 2021: 11; 2022: 12; 2023: 18; 2024: 9; 2025: 11; 2026: 3.

64 papers.

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  1. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  2. 2022Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spacescited by 66
  3. 2022Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoderscited by 58
  4. 2021Deeptime: a Python library for machine learning dynamical models from time series datacited by 36
  5. 2023Sharp Spectral Rates for Koopman Operator Learningcited by 35
  6. 2022Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluationscited by 31
  7. 2022Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimizationcited by 29
  8. 2023Generative learning for nonlinear dynamicscited by 22
  9. 2023Machine Learning for Partial Differential Equationscited by 20
  10. 2023Interpretation of Time-Series Deep Models: A Surveycited by 15
  11. 2023Estimating Koopman operators with sketching to provably learn large scale dynamical systemscited by 15
  12. 2021Chasing Collective Variables using Autoencoders and biased trajectoriescited by 13
38 more
  1. 2021Applying Machine Learning to Study Fluid Mechanicscited by 13
  2. 2023PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operatorcited by 10
  3. 2023Inexact iterative numerical linear algebra for neural network-based spectral estimation and rare-event predictioncited by 9
  4. 2023Differentiable Simulations for Enhanced Sampling of Rare Eventscited by 7
  5. 2024Laplace Transform Based Low-Complexity Learning of Continuous Markov Semigroupscited by 7
  6. 2025Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systemscited by 7
  7. 2022Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectoriescited by 6
  8. 2023Reaction coordinate flows for model reduction of molecular kineticscited by 6
  9. 2023Latent Representation and Simulation of Markov Processes via Time-Lagged Information Bottleneckcited by 6
  10. 2021Deep Learning of Conjugate Mappingscited by 5
  11. 2023Recurrences reveal shared causal drivers of complex time seriescited by 5
  12. 2023Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Datacited by 5
  13. 2021Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertaintiescited by 4
  14. 2022DLKoopman: A deep learning software package for Koopman theorycited by 4
  15. 2025Al-Khwarizmi: Discovering Physical Laws with Foundation Modelscited by 4
  16. 2026Explainable AI: Learning from the Learnerscited by 4
  17. 2021Variational embedding of protein folding simulations using gaussian mixture variational autoencoderscited by 3
  18. 2023Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamicscited by 3
  19. 2023Ophiuchus: Scalable Modeling of Protein Structures through Hierarchical Coarse-graining SO(3)-Equivariant Autoencoderscited by 3
  20. 2023Hierarchical deep learning-based adaptive time-stepping scheme for multiscale simulationscited by 3
  21. 2024Spectral Map for Slow Collective Variables, Markovian Dynamics, and Transition State Ensemblescited by 3
  22. 2024Pushing the Limits of All-Atom Geometric Graph Neural Networks: Pre-Training, Scaling and Zero-Shot Transfercited by 3
  23. 2025Beyond Ensembles: Simulating All-Atom Protein Dynamics in a Learned Latent Spacecited by 3
  24. 2025Koopman Invariants as Drivers of Emergent Time-Series Clustering in Joint-Embedding Predictive Architecturescited by 3
  25. 2021Accelerated Simulations of Molecular Systems through Learning of their Effective Dynamicscited by 2
  26. 2022Automatic Identification of Chemical Moietiescited by 2
  27. 2022Regression-based projection for learning Mori-Zwanzig operatorscited by 2
  28. 2023Understanding recent deep-learning techniques for identifying collective variables of molecular dynamicscited by 2
  29. 2024Machine Learning of Slow Collective Variables and Enhanced Sampling via Spatial Techniquescited by 2
  30. 2021Operator Autoencoders: Learning Physical Operations on Encoded Molecular Graphscited by 1
  31. 2021A purely data-driven framework for prediction, optimization, and control of networked processes: application to networked SIS epidemic modelcited by 1
  32. 2022Heterogeneous mixtures of dictionary functions to approximate subspace invariance in Koopman operatorscited by 1
  33. 2023Enhanced Sampling with Machine Learning: A Reviewcited by 1
  34. 2024Parameter inference from a non-stationary unknown processcited by 1
  35. 2024Intrinsic Dimensionality of Fermi-Pasta-Ulam-Tsingou High-Dimensional Trajectories Through Manifold Learning: A Linear Approachcited by 1
  36. 2025Learning Collective Variables from BioEmu with Time-Lagged Generationcited by 1
  37. 2025Artifacts of Numerical Integration in Learning Dynamical Systemscited by 1
  38. 2025Neural Network Surrogates for Free Energy Computation of Complex Chemical Systemscited by 1

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