Systematic determination of order parameters for chain dynamics using diffusion maps

Ferguson, Andrew L.; Panagiotopoulos, Athanassios Z.; Debenedetti, Pablo G.; Kevrekidis, Ioannis G.

doi:10.1073/pnas.1003293107

Cited by 150 publications

(328 citation statements)

References 59 publications

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“…This makes our definition of a pattern recognition function well-suited for use as a collective variable in accelerated sampling methods, [34] possibly in conjunction with other machine learning techniques to characterize the overall connectivity induced by the selected molecular pattern [35], or similar fingerprint metrics that are guaranteed to distinguish dissimilar structures [36]. The PAMM variables corresponding to different structural descriptor can also be analyzed to yield a coarse-grained, lowdimensional map [37][38][39]. If necessary, one can artificially "soften" the transition between clusters, by dividing all the covariance matrices Σ k in the Gaussian model by a scaling factor α.…”

Section: Analysis Of the Simulationmentioning

confidence: 99%

Recognizing molecular patterns by machine learning: An agnostic structural definition of the hydrogen bond

Gasparotto

Ceriotti

2014

The Journal of Chemical Physics

103

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The concept of chemical bonding can ultimately be seen as a rationalization of the recurring structural patterns observed in molecules and solids. Chemical intuition is nothing but the ability to recognize and predict such patterns, and how they transform into one another. Here we discuss how to use a computer to identify atomic patterns automatically, so as to provide an algorithmic definition of a bond based solely on structural information. We concentrate in particular on hydrogen bonding -a central concept to our understanding of the physical chemistry of water, biological systems and many technologically important materials. Since the hydrogen bond is a somewhat fuzzy entity that covers a broad range of energies and distances, many different criteria have been proposed and used over the years, based either on sophisticate electronic structure calculations followed by an energy decomposition analysis, or on somewhat arbitrary choices of a range of structural parameters that is deemed to correspond to a hydrogen-bonded configuration. We introduce here a definition that is univocal, unbiased, and adaptive, based on our machine-learning analysis of an atomistic simulation. The strategy we propose could be easily adapted to similar scenarios, where one has to recognize or classify structural patterns in a material or chemical compound.

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Section: Analysis Of the Simulationmentioning

confidence: 99%

Recognizing molecular patterns by machine learning: An agnostic structural definition of the hydrogen bond

Gasparotto

Ceriotti

2014

The Journal of Chemical Physics

103

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“…We anticipate that these cooperative transition pathways correspond to a small number of slow collective modes of the halo particle dynamics 15,19,37 . Extracting these slow modes from the simulation trajectory reveals the multi-body transition pathways governing the digital colloid dynamics, and also presents kinetically meaningful collective coordinates in which to construct low-dimensional free energy surface mapping out the accessible morphologies, stable states, and dynamical transition pathways 15,16,18,19,[38][39][40][41] .…”

Section: Digital Colloid Dimensionality Reductionmentioning

confidence: 99%

Section: Digital Colloid Dimensionality Reductionmentioning

confidence: 99%

“…Geometrically, the intrinsic manifold is the low-dimensional phase space volume parameterized by a small number of collective variables that contains the stable colloidal bit states and the dynamic transition pathways between them 15,19,38,39 . Temporally, the existence of the intrinsic manifold can be viewed through the Mori-Zwanzig formalism as the emergence of a small number of slowly-evolving collective coordinates to which the remaining system degrees of freedom are slaved as effective noise 15,19,23,38,39,42 . Compared to linear dimensionality reduction techniques such as principal components analysis (PCA) 43 or multidimensional scaling (MDS) 44 , nonlinear methods provide greater flexibility in extracting collective modes that are nonlinear combinations of the particle degrees of freedom 16,39,45 , enabling the recovery of more general and complex intrinsic manifolds.…”

Section: Digital Colloid Dimensionality Reductionmentioning

confidence: 99%

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Nonlinear machine learning and design of reconfigurable digital colloids

Long

Phillips²,

Jankowksi

et al. 2016

Soft Matter

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Digital colloids, a cluster of freely rotating "halo" particles tethered to the surface of a central particle, were recently proposed as ultra-high density memory elements for information storage. Rational design of these digital colloids for memory storage applications requires a quantitative understanding of the thermodynamic and kinetic stability of the configurational states within which information is stored. We apply nonlinear machine learning to Brownian dynamics simulations of these digital colloids to extract the low-dimensional intrinsic manifold governing digital colloid morphology, thermodynamics, and kinetics. By modulating the relative size ratio between halo particles and central particles, we investigate the size-dependent configurational stability and transition kinetics for the 2-state tetrahedral (N=4) and 30-state octahedral (N=6) digital colloids. We demonstrate the use of this framework to guide the rational design of a memory storage element to hold a block of text that trades off the competing design criteria of memory addressability and volatility. Phone: (217) 300-2354; Fax: (217) 333-2736 † Electronic Supplementary Information (ESI) available: Two movies highlighting the structure and topography of the low-dimensional intrinsic manifolds for the N=4 and N=6 digital colloids, a figure showing the transition network for the N=6 digital colloid, and a movie tracking a N=6 transition event over the intrinsic manifold. See

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“…as a result of bond rotations or steric interactions. [12][13][14] Advances in the field of statistical learning, notably in nonlinear dimensionality reduction (NLDR) techniques, [15][16][17] were quickly embraced by the molecular simulation community to visualize trajectories, realizing that conformations often evolve close to a nonlinear manifold often called intrinsic manifold, [18][19][20][21][22] 24 or LSDMap. 25 Building on these techniques, a number of methods have been developed to systematically define differentiable and nonlinear CVs, to be used in enhanced sampling simulations.…”

mentioning

confidence: 99%

Topological obstructions in the way of data-driven collective variables

Hashemian

Arroyo

2015

The Journal of Chemical Physics

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Nonlinear dimensionality reduction (NLDR) techniques are increasingly used to visualize molecular trajectories and to create data-driven collective variables for enhanced sampling simulations. The success of these methods relies on their ability to identify the essential degrees of freedom characterizing conformational changes. Here, we show that NLDR methods face serious obstacles when the underlying collective variables present periodicities, e.g. arising from proper dihedral angles. As a result, NLDR methods collapse very distant configurations, thus leading to misinterpretations and inefficiencies in enhanced sampling. Here, we identify this largely overlooked problem and discuss possible approaches to overcome it. We also characterize the geometry and topology of conformational changes of alanine dipeptide, a benchmark system for testing new methods to identify collective variables.PACS numbers: 87.10. Tf, 87.15.hp Thanks to enhanced sampling techniques, it is possible to connect molecular conformations separated by high energy barriers, and accurately compute free energies in systems exhibiting metastability. The success of these techniques relies on a good set of collective variables (CVs), capturing the metastability of the system with a few degrees of freedom. CVs are commonly chosen out of experience or physical intuition. As increasingly complex systems become accessible computationally, 1 the task of selecting appropriate CVs becomes highly nontrivial. 2 This situation has motivated in recent years intense research aimed at systematic and data-driven approaches to select CVs, often relying on statistical learning methods. In particular, dimensionality reduction techniques automatically identify a reduced set of coordinates capturing the essential behavior of a complex system, starting from a pre-existing ensemble of molecular configurations, called training set.The most widespread dimensionality reduction method is principal component analysis (PCA). 3 PCA is a linear method, which selects mutually orthogonal directions such that, by projecting the data onto a few of them, the variance of the projected data is maximized. PCA has been widely applied to characterize the essential dynamics, 4-8 understand molecular flexibility 9 and enhance sampling in molecular dynamics. 10,11 PCA and in general linear dimensionality reduction methods are very popular because of their simplicity. However, they fail to identify nonlinear correlations in the data, which are often present in molecular systems, e.g. as a result of bond rotations or steric interactions. [12][13][14] Advances in the field of statistical learning, notably in nonlinear dimensionality reduction (NLDR) techniques, 15-17 were quickly embraced by the molecular simulation community to visualize trajectories, realizing that conformations often evolve close to a nonlinear manifold often called intrinsic manifold, 18-22 although some systems evolve on non-manifold sets. 23 Difa) Electronic

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Systematic determination of order parameters for chain dynamics using diffusion maps

Cited by 150 publications

References 59 publications

Recognizing molecular patterns by machine learning: An agnostic structural definition of the hydrogen bond

Recognizing molecular patterns by machine learning: An agnostic structural definition of the hydrogen bond

Nonlinear machine learning and design of reconfigurable digital colloids

Topological obstructions in the way of data-driven collective variables

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