Coarse-graining molecular systems by spectral matching

Nüske, Feliks; Boninsegna, Lorenzo; Clementi, Cecilia

doi:10.1063/1.5100131

Cited by 33 publications

(38 citation statements)

References 64 publications

(93 reference statements)

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“…Furthermore, is it possible to learn coarse-grained dynamics by only considering the dominant terms of the decomposition of the system's equations into eigenvalues, eigenfunctions, and modes (cf. Example 3.3 and also [43])? Another interesting application of gEDMD would be to compute committor functions or hitting times.…”

Section: Resultsmentioning

confidence: 96%

Data-driven approximation of the Koopman generator: Model reduction, system identification, and control

Klus

Nüske

Peitz

et al. 2020

Physica D: Nonlinear Phenomena

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187

160

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We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions, and modes of the generator and for system identification. In addition to learning the governing equations of deterministic systems, which then reduces to SINDy (sparse identification of nonlinear dynamics), it is possible to identify the drift and diffusion terms of stochastic differential equations from data. Moreover, we apply gEDMD to derive coarse-grained models of high-dimensional systems, and also to determine efficient model predictive control strategies. We highlight relationships with other methods and demonstrate the efficacy of the proposed methods using several guiding examples and prototypical molecular dynamics problems. arXiv:1909.10638v1 [math.DS] 23 Sep 2019Most of the aforementioned techniques turn out to be strongly related, with the unifying concept being Koopman operator theory [16,17,18]. In what follows, we will focus mainly on the generator of the Koopman operator and its properties and applications. SINDy [5] constitutes a milestone for data-driven discovery of dynamical systems. Because of the close relationship between the vector field of a deterministic dynamical system and its Koopman generator, SINDy is a special case of the framework we will introduce in this study. In [19,20], the authors presented an extension of SINDy to determine eigenfunctions of the Koopman generator. The discovered eigenfunctions are then used for control, resulting in the so-called KRONIC framework. Another extension of SINDy was derived in [21], allowing for the identification of parameters of a stochastic system using Kramers-Moyal formulae.A different avenue towards system identification was taken in [22,23]. Here, the Koopman operator is first approximated with the aid of EDMD, and then its generator is determined using the matrix logarithm. Subsequently, the right-hand side of the differential equation is extracted from the matrix representation of the generator. The relationship between the Koopman operator and its generator was also exploited in [24] for parameter estimation of stochastic differential equations.A method for computing eigenfunctions of the Koopman generator was proposed in [25], where the diffusion maps algorithm is used to set up a Galerkin-projected eigenvalue problem with orthogonal basis elements. Two efficient methods for computing the generator of the adjoint Perron-Frobenius operator based on Ulam's method and spectral collocation were presented in [26]. Provided that a model of the system dynamics is available, the computation of trajectories can be replaced by evaluations of the right-hand side of the system, which is often orders of magnitude faster.The purpose of this study is to present a general framework to compute a matrix approximation of the Koop...

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Section: Resultsmentioning

confidence: 96%

Data-driven approximation of the Koopman generator: Model reduction, system identification, and control

Klus

Nüske

Peitz

et al. 2020

Physica D: Nonlinear Phenomena

Self Cite

187

160

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“…The development of variational approaches that target dynamical properties of the model represents a significant step towards not only more systematic investigations into the optimization of these models but also a better fundamental understanding of the required forces for reproducing particular properties. However, despite the development of several elegant theoretical frameworks [76,81,161], there seems to be a lack of applications to molecular systems. It is currently unclear whether this is due to practical difficulties of the approaches or simply a lack of adoption from external researchers.…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…Through the consideration of one-and two-site per amino acid representations, the results highlight the importance of local frustration in reproducing the dominant features of the folding landscape. Very recently Nüske et al [161] have proposed a "spectral matching" method, which attempts to parametrize a CG potential to accurately represent the long time scale processes by targeting the dominant eigenfunctions of the system's dynamical propagator. This method utilizes the variational approach to conformational dynamics [152,153] along with methods for parameter estimation for stochastic dynamics [162].…”

Section: B Markov State Models (Msms)mentioning

confidence: 99%

Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties

Rudzinski

2019

Computation

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Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes, bottom-up CG models are systematically constructed from a higher-resolution model to retain a high level of chemical specificity. The removal of degrees of freedom from the system modifies the relationship between the relative time scales of distinct dynamical processes through both a loss of friction and a "smoothing" of the free-energy landscape. While these effects typically result in faster dynamics, decreasing the computational expense of the model, they also obscure the connection to the true dynamics of the system. The lack of consistent dynamics is a serious limitation for CG models, which not only prevents quantitatively accurate predictions of dynamical observables but can also lead to qualitatively incorrect descriptions of the characteristic dynamical processes. With many methods available for optimizing the structural and thermodynamic properties of chemically-specific CG models, recent years have seen a stark increase in investigations addressing the accurate description of dynamical properties generated from CG simulations. In this review, we present an overview of these efforts, ranging from bottom-up parametrizations of generalized Langevin equations to refinements of the CG force field based on a Markov state modeling framework. We aim to make connections between seemingly disparate approaches, while laying out some of the major challenges as well as potential directions for future efforts.

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“…While coarse-grained MD models may perform well in reproducing the thermodynamics of the atomistic system, they may fail in reproducing the kinetics. Existing approaches include adding fictitious particles [138], or training the coarse-grained model with spectral matching [139]. There is indication that the kinetics can be approximately up to a global scaling factor in barrier-crossing problems when the barriers are well approximated [140], which could be achieved by identifying the slow reaction coordinates [59], and assigning more weight to the transition state in force matching or relative entropy minimization.…”

Section: Kinetics Of Coarse-grained Modelsmentioning

confidence: 99%

Machine Learning for Molecular Simulation

Noé

Tkatchenko

Müller

et al. 2020

Annu. Rev. Phys. Chem.

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631

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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Coarse-graining molecular systems by spectral matching

Cited by 33 publications

References 64 publications

Data-driven approximation of the Koopman generator: Model reduction, system identification, and control

Data-driven approximation of the Koopman generator: Model reduction, system identification, and control

Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties

Machine Learning for Molecular Simulation

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