Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning

Noé, Frank; Olsson, Simon; Köhler, Jonas; Wu, Hao

doi:10.1126/science.aaw1147

Cited by 560 publications

(568 citation statements)

References 50 publications

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“…If the aim is to learn a probability distribution from sampling data (density estimation) or learn to efficiently sample from a given probability distribution (Boltzmann generation [37]), one typically faces the challenge of matching the probability distribution of the trained model with a reference.…”

Section: Sampling and Thermodynamicsmentioning

confidence: 99%

“…In Boltzmann generation [37], we aim to efficiently sample the equilibrium distribution µ(x) of a many-body system defined by its energy function u(x) (Eq. 1).…”

Section: Sampling and Thermodynamicsmentioning

confidence: 99%

“…Classical MD force fields define bonded interactions by assigning atoms to nodes in a bond graph, and thus exchanging of individual atom pairs no longer preserves the energy. However, the energy is still invariant to the exchange of identical molecules, e.g., solvent, and is important to take that into account for coarse-graining [18] and generating samples from the equilibrium density [37].…”

Section: Permutational Invariance/equivariancementioning

confidence: 99%

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Machine Learning for Molecular Simulation

Noé

Tkatchenko

Müller

et al. 2020

Annu. Rev. Phys. Chem.

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672

476

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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...

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Section: Sampling and Thermodynamicsmentioning

confidence: 99%

“…In Boltzmann generation [37], we aim to efficiently sample the equilibrium distribution µ(x) of a many-body system defined by its energy function u(x) (Eq. 1).…”

Section: Sampling and Thermodynamicsmentioning

confidence: 99%

Section: Permutational Invariance/equivariancementioning

confidence: 99%

See 1 more Smart Citation

Machine Learning for Molecular Simulation

Noé

Tkatchenko

Müller

et al. 2020

Annu. Rev. Phys. Chem.

Self Cite

672

476

View full text Add to dashboard Cite

show abstract

“…Specifically, it can accelerate (i) parameter estimation, (ii) uncertainty quantification, and (iii) dimensionality reduction, three of the most common post-processing tasks from a biophysical simulation. Incorporating specific biophysical model information like stress-strain relationships [113] or statistical molecular dynamic states [114] into ML algorithms can also reduce the computational time for numerical solvers. Finally, more standard ML approaches like clustering and dimensionality reduction can assist in both visualization and interpretation of simulation results.…”

Section: Applications Of ML For Meshing Simulation and Data Analysismentioning

confidence: 99%

Applications and Challenges of Machine Learning to Enable Realistic Cellular Simulations

et al. 2020

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In this perspective, we examine three key aspects of an end-to-end pipeline for realistic cellular simulations: reconstruction and segmentation of cellular structures; generation of cellular structures; and mesh generation, simulation, and data analysis. We highlight some of the relevant prior work in these distinct but overlapping areas, with a particular emphasis on current use of machine learning technologies, as well as on future opportunities.

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“…As many systems exist that have high energy barriers solving the problem of broken ergodicity has been of high interest and several algorithms have been proposed [6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Funnel hopping Monte Carlo: An efficient method to overcome broken ergodicity

Finkler

Goedecker

2020

The Journal of Chemical Physics

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Monte Carlo simulations are a powerful tool to investigate the thermodynamic properties of atomic systems. In practice however, sampling of the complete configuration space is often hindered by high energy barriers between different regions of configuration space which can make ergodic sampling completely infeasible within accessible simulation times. Although several extensions to the conventional Monte Carlo scheme have been developed, that enable the treatment of such systems, these extensions often entail substantial computational cost or rely on the harmonic approximation. In this work we propose an exact method called Funnel Hopping Monte Carlo (FHMC) that is inspired by the the ideas of smart darting but is more efficient. Gaussian mixtures are used to approximate the Boltzmann distribution around local energy minima which are then used to propose high quality Monte Carlo moves that enable the Monte Carlo simulation to directly jump between different funnels. To fit the Gaussian mixtures we developed an extended version of the expectationmaximization algorithm that is able to take advantage of the high symmetry present in many low energy configurations.We demonstrate the methods performance on the example of the 38 as well as the 75 atom Lennard-Jones clusters which are well known for their double funnel energy landscapes that prevent ergodic sampling with conventional Monte Carlo simulations. By integrating FHMC into the parallel tempering scheme we were able to reduce the number of steps required until convergence of the simulation significantly. This gain in efficieny of about two orders of magnitude will make it finally possible to perform high accuracy Monte Carlo simulations at the level of density functional theory.This paper was submitted to the Journal of Chemical Physics.I.

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Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning

Cited by 560 publications

References 50 publications

Machine Learning for Molecular Simulation

Machine Learning for Molecular Simulation

Applications and Challenges of Machine Learning to Enable Realistic Cellular Simulations

Funnel hopping Monte Carlo: An efficient method to overcome broken ergodicity

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