Data-driven Computation of Molecular Reaction Coordinates

Please always quote using this URN: urn:nbn:de:0297-zib-66179
  • The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics is characterized by rare or slow transition events. In a recent publication, the authors identified a condition under which such reaction coordinates exist - the existence of a so-called transition manifold - and proposed a numerical method for their point-wise computation that relies on short bursts of MD simulations. This article represents an extension of the method towards practical applicability in computational chemistry. It describes an alternative computational scheme that instead relies on more commonly available types of simulation data, such as single long molecular trajectories, or the push-forward of arbitrary canonically-distributed point clouds. It is based on a Galerkin approximation of the transition manifold reaction coordinates, that can be tuned to individual requirements by the choice of the Galerkin ansatz functions. Moreover, we propose a ready-to-implement variant of the new scheme, that computes data-fitted, mesh-free ansatz functions directly from the available simulation data. The efficacy of the new method is demonstrated on a realistic peptide system.

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Author:Andreas Bittracher, Ralf Banisch, Christof Schütte
Document Type:ZIB-Report
Tag:Galerkin method; coarse graining; data-driven; meshfree basis; reaction coordinate; transfer operator; transition manifold
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H35 Computational methods for stochastic equations [See also 65C30]
70-XX MECHANICS OF PARTICLES AND SYSTEMS (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX) / 70Kxx Nonlinear dynamics [See also 34Cxx, 37-XX] / 70K70 Systems with slow and fast motions
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]
Date of first Publication:2017/12/18
Series (Serial Number):ZIB-Report (17-77)