Enhanced, targeted sampling of high-dimensional free-energy landscapes using variationally enhanced sampling, with an application to chignolin

Shaffer, Patrick; Valsson, Ómar; Parrinello, Michele

doi:10.1073/pnas.1519712113

Cited by 58 publications

(95 citation statements)

References 55 publications

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“…Contrary to metadynamics and other similar methods, VES does not generate the bias potential by periodically adding on the fly small contributions, but as the result of the minimization of a convex functional. Various extensions have been proposed, where VES has been used in different ways (17)(18)(19)(20)(21)(22). Let us suppose that the physical behavior of interest is well described by a set of CVs s = s(R), which are function of the coordinates R of the N particles that compose the system.…”

Section: Variationally Enhanced Samplingmentioning

confidence: 99%

Coarse graining from variationally enhanced sampling applied to the Ginzburg–Landau model

Invernizzi

Valsson

Parrinello

2017

Proc. Natl. Acad. Sci. U.S.A.

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A powerful way to deal with a complex system is to build a coarsegrained model capable of catching its main physical features, while being computationally affordable. Inevitably, such coarsegrained models introduce a set of phenomenological parameters, which are often not easily deducible from the underlying atomistic system. We present a unique approach to the calculation of these parameters, based on the recently introduced variationally enhanced sampling method. It allows us to obtain the parameters from atomistic simulations, providing thus a direct connection between the microscopic and the mesoscopic scale. The coarsegrained model we consider is that of Ginzburg-Landau, valid around a second-order critical point. In particular, we use it to describe a Lennard-Jones fluid in the region close to the liquidvapor critical point. The procedure is general and can be adapted to other coarse-grained models.coarse graining | enhanced sampling | Ginzburg-Landau free energy | second-order phase transitions | Lennard-Jones C omputer simulations of condensed systems based on an atomistic description of matter are playing an everincreasing role in many fields of science. However, as the complexity of the systems studied increases, so does the awareness that a less detailed, but nevertheless accurate, description of the system is necessary.This has been long since recognized, and branches of physics like elasticity or hydrodynamics can be classified in modern terms as coarse-grained (CG) models of matter. In more recent times, a field theoretical model suitable to describe second-order phase transitions has been introduced by Landau (1) and later perfected by Ginzburg (2). In recent decades a number of coarsegrained models that aim at describing polymers or biomolecules have also been proposed (3,4). In all these approaches some degrees of freedom, deemed not essential to study the phenomenon at hand, are integrated out and the resulting reduced description contains a number of parameters that are not easily determined.Here we use the recently developed variationally enhanced sampling (VES) method (5) to suggest a procedure that allows the determination of such parameters, starting from the microscopic Hamiltonian. This illuminates a somewhat unexpected application of VES, which has been introduced as an enhanced sampling method. We show that it also provides a powerful framework for the optimization of CG models, due to the combination of its enhanced sampling capabilities and its variational flexibility. Moreover, VES takes advantage of its deep connection with relative entropy, a quantity that has been shown to play a key role in multiscale problems (6, 7).As a first test case for our procedure we consider the Ginzburg-Landau (GL) model for continuous phase transitions. An advantage of using this model is that its strengths and limits are well known and that other researchers have already attempted to perform such a calculation (8)(9)(10)(11)(12)(13)(14). A system that undergoes a second-order phase transition is desc...

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Section: Variationally Enhanced Samplingmentioning

confidence: 99%

Coarse graining from variationally enhanced sampling applied to the Ginzburg–Landau model

Invernizzi

Valsson

Parrinello

2017

Proc. Natl. Acad. Sci. U.S.A.

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“…Thus well-tempered metadynamics implicitly introduced the possibility of choosing a non-uniform target distribution. The idea of aiming at a specific target distribution has been later generalized [14] and various possibilities have been explored [15][16][17][18], in particular within the framework of variationally enhanced sampling (VES) method [19]. This is an often overlooked point, especially in AUSlike methods.…”

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confidence: 99%

Rethinking Metadynamics: From Bias Potentials to Probability Distributions

Invernizzi

Parrinello

2020

J. Phys. Chem. Lett.

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185

270

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Metadynamics is an enhanced sampling method of great popularity, based on the on-the-fly construction of a bias potential that is function of a selected number of collective variables. We propose here a drastic change in perspective that shifts the focus from the bias to the probability distribution reconstruction, leading to an improvement in usability and convergence speed. The resulting enhanced sampling method can be seen as a combination of metadynamics and adaptive umbrella sampling approaches, that aims at taking the best from the two worlds. This new method has a straightforward reweighting scheme and allows for efficient importance sampling, avoiding uninteresting high free energy regions. Thanks to a compressed kernel density estimation it can handle a higher dimensional collective variable space, and does not require any prior knowledge of the boundaries of such space. The new method comes in two variants. The first aims at a quick convergence, avoiding oscillations and maximizing the quasi-static bias regime, while in the second the main focus is on a rapid exploration of the free energy landscape. We demonstrate the performance of the method in a number of representative examples.Enhanced sampling plays a crucial role in modern simulation techniques, and is a very active area of research [1]. Of particular importance has been the work of Torrie and Valleau [2]. They consider a system with an interaction potential U (R), where R denotes the atomic coordinates. Sampling is accelerated by adding a bias potential V (s) that depends on R via a set of collective variables (CVs), s = s(R). The CVs are chosen so as to describe the modes of the system that are more difficult to sample. The choice of a proper set of CVs is critical, as it determines the efficiency of the method. The properties of the unbiased system are then calculated by using a reweighting procedure. In fact the unbiased probability densitycan be written as an average over the biased ensemble:where β is the inverse temperature. Since this work, a large number of CV based methods have been proposed. Adaptive umbrella sampling[3] (AUS) was the first to build iteratively V (s) so that it would compensate for the free energy surface (FES), F (s) = − 1 β log P (s). At the n-th iteration the bias is given by:where the probability estimate P n (s) can be obtained via a weighted histogram, with weights w k = e βV k , or some more elaborate estimator [4], and can be updated iteratively or on the fly [5,6]. At convergence one has V (s) = −F (s). A different approach has been introduced by metadynamics[7, 8] (MetaD). Here one builds V (s) directly, instead of first reconstructing the probability distribution. The bias is updated on the fly by adding a Gaussian centered at every new point sampled s k :

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“…This bias potential floods the free energy surface up to a predefined energy level. By construction this approach guarantees bias free transition states and accurate times can be extracted using equation (16). We point out that the independence of F (n) from the system size provides a strong encouragement to limit ourselves to the study of small systems.…”

Section: Discussionmentioning

confidence: 99%

A variational approach to nucleation simulation

2016

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We study by computer simulation the nucleation of a supersaturated Lennard-Jones vapor into the liquid phase. The large free energy barriers to transition make the time scale of this process impossible to study by ordinary molecular dynamics simulations. Therefore we use a recently developed enhanced sampling method [Valsson and Parrinello, Phys. Rev. Lett.113, 090601 (2014)] based on the variational determination of a bias potential. We differ from previous applications of this method in that the bias is constructed on the basis of the physical model provided by the classical theory of nucleation. We examine the technical problems associated with this approach. Our results are very satisfactory and will pave the way for calculating the nucleation rates in many systems.

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Enhanced, targeted sampling of high-dimensional free-energy landscapes using variationally enhanced sampling, with an application to chignolin

Cited by 58 publications

References 55 publications

Coarse graining from variationally enhanced sampling applied to the Ginzburg–Landau model

Coarse graining from variationally enhanced sampling applied to the Ginzburg–Landau model

Rethinking Metadynamics: From Bias Potentials to Probability Distributions

A variational approach to nucleation simulation

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