# Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics

arXiv: https://arxiv.org/abs/2307.00365 · HTML: https://mlsanity.com/paper/2307.00365/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 52 references that are in the map.
- First posted on arXiv 1 Jul 2023.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics](https://mlsanity.com/paper/1710.11239/) (2017)
- [Variational approach for learning Markov processes from time series data](https://mlsanity.com/paper/1707.04659/) (2017)
- [Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape exploration](https://mlsanity.com/paper/1801.00203/) (2017)
- [Variational Encoding of Complex Dynamics](https://mlsanity.com/paper/1711.08576/) (2017)
- [Variational Koopman models: slow collective variables and molecular kinetics from short off-equilibrium simulations](https://mlsanity.com/paper/1610.06773/) (2016)
- [Nonlinear Discovery of Slow Molecular Modes using State-Free Reversible VAMPnets](https://mlsanity.com/paper/1902.03336/) (2019)
- [Interpretable Embeddings From Molecular Simulations Using Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1912.12175/) (2019)
- [Chasing Collective Variables using Autoencoders and biased trajectories](https://mlsanity.com/paper/2104.11061/) (2021)
- [Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks](https://mlsanity.com/paper/2110.14523/) (2021)
- [Capabilities and Limitations of Time-lagged Autoencoders for Slow Mode Discovery in Dynamical Systems](https://mlsanity.com/paper/1906.00325/) (2019)

## Built on by (most cited first, 2 of 2)

- [Learning collective variables that preserve transition rates](https://mlsanity.com/paper/2506.01222/) (2025)
- [Effective Dynamics and Transition Pathways from Koopman-Inspired Neural Learning of Collective Variables](https://mlsanity.com/paper/2604.05778/) (2026)

## Abstract (arXiv)

High-dimensional metastable molecular system can often be characterised by a few features of the system, i.e. collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning-based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning-based approaches for finding CVs, either by computing leading eigenfunctions of infinitesimal generator or transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples.