Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations

Wu, Hao; Nüske, Feliks; Paul, Fabian; Klus, Stefan; Koltai, Péter; Noé, Frank

doi:10.1063/1.4979344

Cited by 123 publications

(196 citation statements)

References 86 publications

(167 reference statements)

Supporting

Mentioning

195

Contrasting

Order By: Relevance

“…A common approach in MD, but also in other fields such as dynamical systems and fluid mechanics, is to seek a pair (E, P), such that P is a small matrix that propagates state vectors in a Markovian (memoryless) fashion [76,77,78,79,74,80,81,82,83,84,73]. This is motivated by the spectral decomposition of dynamics (Eq.…”

Section: Kineticsmentioning

confidence: 99%

Machine Learning for Molecular Simulation

Noé

Tkatchenko

Müller

et al. 2020

Annu. Rev. Phys. Chem.

Self Cite

631

476

View full text Add to dashboard Cite

Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for a machine learning revolution and have already been profoundly impacted by the application of existing ML methods. Here we review recent ML methods for molecular simulation, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, coarse-grained molecular dynamics, the extraction of free energy surfaces and kinetics and generative network approaches to sample molecular equilibrium structures and compute thermodynamics. To explain these methods and illustrate open methodological problems, we review some important principles of molecular physics and describe how they can be incorporated into machine learning structures. Finally, we identify and describe a list of open challenges for the interface between ML and molecular simulation. 1 arXiv:1911.02792v1 [physics.chem-ph] 7 Nov 2019 complex relationship between the input (the pixels) and the output (the labels) that is unknown in its explicit form but can be inferred by a suitable algorithm. Clearly, such an operating principle can be very useful in the description of atomic and molecular systems as well. We know that atomistic configurations dictate the chemical properties, and the machine can learn to associate the latter to the former without solving first principle equations, if presented with enough examples. Although different machine learning tools are available and have been applied to molecular simulation (e.g., kernel methods [2]), here we mostly focus on the use of neural networks, now often synonymously used with the term "deep learning". We assume the reader has basic knowledge of machine learning and we refer to the literature for an introduction to statistical learning theory [3,4] and deep learning [5,6].One of the first applications of machine learning in Chemistry has been to extract classical potential energy surfaces from quantum mechanical (QM) calculations, in order to efficiently perform molecular dynamics (MD) simulations that can incorporate quantum effects. The seminal work of Behler and Parrinello in this direction [7] has opened the way to a now rapidly advancing area of research [8,9,10,11,12,13,14,15]. In addition to atomistic force fields, it has been recently shown that, in the same spirit, effective molecular models at resolution coarser than atomistic can be designed by ML [16,17,18]. Analysis and simulation of MD trajectories has also been affected by ML, for instance for the definition of optimal reaction coordinates [19,20,21,22,23,24], the estimate of free energy surfaces [25,26,27,22], the construction of Markov State Models [21,23,28], and for enhancing MD sampling by learning bias potentials [29,30,31,32,33] or selecting starting configurations by active learning [34,35,36]. Finally, ML can be used to generate samples from the equilibrium distribution of a molecular system without performing MD altogether, as proposed...

show abstract

Section: Kineticsmentioning

confidence: 99%

Machine Learning for Molecular Simulation

Noé

Tkatchenko

Müller

et al. 2020

Annu. Rev. Phys. Chem.

Self Cite

631

476

View full text Add to dashboard Cite

show abstract

“…The matrix K is a finite-dimensional linear approximation to the continuous integral Koopman operator K and can be called the Koopman matrix 4,5,14,[49][50][51] . In the time-lagged context, the operator propagates a view of the system at time t to a possibly different view of the system at time t+τ .…”

Section: Appendix C: Connection To Koopman Operator Approximationmentioning

confidence: 99%

Deflation reveals dynamical structure in nondominant reaction coordinates

Husic

Noé

2019

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

The output of molecular dynamics simulations is high-dimensional, and the degrees of freedom among the atoms are related in intricate ways. Therefore, a variety of analysis frameworks have been introduced in order to distill complex motions into lower-dimensional representations that model the system dynamics. These dynamical models have been developed to optimally approximate the system's global kinetics. However, the separate aims of optimizing global kinetics and modeling a process of interest diverge when the process of interest is not the slowest process in the system. Here, we introduce deflation into state-of-the-art methods in molecular kinetics in order to preserve the use of variational optimization tools when the slowest dynamical mode is not the same as the one we seek to model and understand. First, we showcase deflation for a simple toy system and introduce the deflated variational approach to Markov processes (dVAMP). Using dVAMP, we show that nondominant reaction coordinates produced using deflation are more informative than their counterparts generated without deflation. Then, we examine a protein folding system in which the slowest dynamical mode is not folding. Following a dVAMP analysis, we show that deflation can be used to obscure this undesired slow process from a kinetic model, in this case a VAMPnet. The incorporation of deflation into current methods opens the door for enhanced sampling strategies and more flexible, targeted model building.arXiv:1907.04101v1 [q-bio.BM]

show abstract

“…Although we typically have stationary dynamics in MD datasets, we use the VAMP because we do not need to enforce reversibility in the dynamics as in the VAC, nor do we need to perform the statistically unfavorable reweighting 53 described in Ref. 37. For the VAMP, we require the following three covariance matrices:…”

Section: Estimating Koopman Matrix and Vamp Scorementioning

confidence: 99%

“…This changed in 2013, when Noé and Nüske presented a variational principle that quantifies how well a given set of coordinates, features or a given MSM resolve the Markov operator eigenfunctions, and thus the slowest processes 28,29 . This variational approach to conformational dynamics (VAC) has been highly developed in the past five years: time-lagged independent component analysis (TICA), an algorithm devised in machine learning 30 , has been shown to be the optimal linear approximator to the Markov operator eigenfunctions 31 ; an em-bedding of the eigenfunctions approximated by the VAC or TICA into a kinetic map has been proposed, in which distances are related to transition times 32,33 ;and hierarchical 34 and kernel-based estimators 35,36 have been developed, as well as methods to estimate VAC/TICA from short off-equilibrium trajectories 37 . Recently, the VAC has been generalized to the variational approach for Markov processes (VAMP), which can accommodate nonreversible dynamics 38 .…”

Section: Introductionmentioning

confidence: 99%

Variational selection of features for molecular kinetics

Scherer

Husic

Hoffmann

et al. 2019

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

The modeling of atomistic biomolecular simulations using kinetic models such as Markov state models (MSMs) has had many notable algorithmic advances in recent years. The variational principle has opened the door for a nearly fully automated toolkit for selecting models that predict the long-timescale kinetics from molecular dynamics simulations. However, one yet-unoptimized step of the pipeline involves choosing the features, or collective variables, from which the model should be constructed. In order to build intuitive models, these collective variables are often sought to be interpretable and familiar features, such as torsional angles or contact distances in a protein structure. However, previous approaches for evaluating the chosen features rely on constructing a full MSM, which in turn requires additional hyperparameters to be chosen, and hence leads to a computationally expensive framework. Here, we present a method to optimize the feature choice directly, without requiring the construction of the final kinetic model. We demonstrate our rigorous preprocessing algorithm on a canonical set of twelve fast-folding protein simulations, and show that our procedure leads to more efficient model selection.

show abstract

Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations

Cited by 123 publications

References 86 publications

Machine Learning for Molecular Simulation

Machine Learning for Molecular Simulation

Deflation reveals dynamical structure in nondominant reaction coordinates

Variational selection of features for molecular kinetics

Contact Info

Product

Resources

About