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

arXiv: https://arxiv.org/abs/1710.11239 · HTML: https://mlsanity.com/paper/1710.11239/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2017.

## Built on by (most cited first, 30 of 65)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2205.14027/) (2022)
- [Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders](https://mlsanity.com/paper/2201.05136/) (2022)
- [Deeptime: a Python library for machine learning dynamical models from time series data](https://mlsanity.com/paper/2110.15013/) (2021)
- [Sharp Spectral Rates for Koopman Operator Learning](https://mlsanity.com/paper/2302.02004/) (2023)
- [Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations](https://mlsanity.com/paper/2207.06503/) (2022)
- [Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimization](https://mlsanity.com/paper/2206.00176/) (2022)
- [Generative learning for nonlinear dynamics](https://mlsanity.com/paper/2311.04128/) (2023)
- [Machine Learning for Partial Differential Equations](https://mlsanity.com/paper/2303.17078/) (2023)
- [Interpretation of Time-Series Deep Models: A Survey](https://mlsanity.com/paper/2305.14582/) (2023)
- [Estimating Koopman operators with sketching to provably learn large scale dynamical systems](https://mlsanity.com/paper/2306.04520/) (2023)
- [Chasing Collective Variables using Autoencoders and biased trajectories](https://mlsanity.com/paper/2104.11061/) (2021)
- [Applying Machine Learning to Study Fluid Mechanics](https://mlsanity.com/paper/2110.02083/) (2021)
- [PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator](https://mlsanity.com/paper/2306.12962/) (2023)
- [Inexact iterative numerical linear algebra for neural network-based spectral estimation and rare-event prediction](https://mlsanity.com/paper/2303.12534/) (2023)
- [Differentiable Simulations for Enhanced Sampling of Rare Events](https://mlsanity.com/paper/2301.03480/) (2023)
- [Laplace Transform Based Low-Complexity Learning of Continuous Markov Semigroups](https://mlsanity.com/paper/2410.14477/) (2024)
- [Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2505.18671/) (2025)
- [Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectories](https://mlsanity.com/paper/2209.09977/) (2022)
- [Reaction coordinate flows for model reduction of molecular kinetics](https://mlsanity.com/paper/2309.05878/) (2023)
- [Latent Representation and Simulation of Markov Processes via Time-Lagged Information Bottleneck](https://mlsanity.com/paper/2309.07200/) (2023)
- [Deep Learning of Conjugate Mappings](https://mlsanity.com/paper/2104.01874/) (2021)
- [Recurrences reveal shared causal drivers of complex time series](https://mlsanity.com/paper/2301.13516/) (2023)
- [Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Data](https://mlsanity.com/paper/2306.10275/) (2023)
- [Al-Khwarizmi: Discovering Physical Laws with Foundation Models](https://mlsanity.com/paper/2502.01702/) (2025)
- [Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertainties](https://mlsanity.com/paper/2106.06033/) (2021)
- [DLKoopman: A deep learning software package for Koopman theory](https://mlsanity.com/paper/2211.08992/) (2022)
- [Koopman Invariants as Drivers of Emergent Time-Series Clustering in Joint-Embedding Predictive Architectures](https://mlsanity.com/paper/2511.09783/) (2025)
- [Explainable AI: Learning from the Learners](https://mlsanity.com/paper/2601.05525/) (2026)
- [Variational embedding of protein folding simulations using gaussian mixture variational autoencoders](https://mlsanity.com/paper/2108.12493/) (2021)

## 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.