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Riemann metric approach to optimal sampling of multidimensional free-energy landscapes
KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Physics.
KTH, Centres, SeRC - Swedish e-Science Research Centre.ORCID iD: 0000-0002-9881-7857
KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Physics.ORCID iD: 0000-0002-7498-7763
2018 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 98, no 2, article id 023312Article in journal (Refereed) Published
Abstract [en]

Exploring the free-energy landscape along reaction coordinates or system parameters λ is central to many studies of high-dimensional model systems in physics, e.g., large molecules or spin glasses. In simulations this usually requires sampling conformational transitions or phase transitions, but efficient sampling is often difficult to attain due to the roughness of the energy landscape. For Boltzmann distributions, crossing rates decrease exponentially with free-energy barrier heights. Thus, exponential acceleration can be achieved in simulations by applying an artificial bias along λ tuned such that a flat target distribution is obtained. A flat distribution is, however, an ambiguous concept unless a proper metric is used and is generally suboptimal. Here we propose a multidimensional Riemann metric, which takes the local diffusion into account, and redefine uniform sampling such that it is invariant under nonlinear coordinate transformations. We use the metric in combination with the accelerated weight histogram method, a free-energy calculation and sampling method, to adaptively optimize sampling toward the target distribution prescribed by the metric. We demonstrate that for complex problems, such as molecular dynamics simulations of DNA base-pair opening, sampling uniformly according to the metric, which can be calculated without significant computational overhead, improves sampling efficiency by 50%-70%.

Place, publisher, year, edition, pages
American Physical Society , 2018. Vol. 98, no 2, article id 023312
Keywords [en]
Bioinformatics, Boltzmann equation, Computational chemistry, Mathematical transformations, Molecular dynamics, Reaction kinetics, Boltzmann distribution, Computational overheads, Conformational transitions, Free-energy calculations, High-dimensional models, Molecular dynamics simulations, Multidimensional free energy, Nonlinear coordinate transformation, Free energy
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-236741DOI: 10.1103/PhysRevE.98.023312ISI: 000443145500007PubMedID: 30253489Scopus ID: 2-s2.0-85052735453OAI: oai:DiVA.org:kth-236741DiVA, id: diva2:1257566
Note

Export Date: 22 October 2018; Article; Correspondence Address: Hess, B.; Department of Physics, Swedish E-Science Research Center, KTH Royal Institute of TechnologySweden; email: hess@kth.se; Funding details: HPC2N; Funding details: SNIC 2016/10-47; Funding details: 2017/11-25; Funding details: 2016/1-562; Funding details: 258980, ERC, European Research Council; Funding details: 2014-4505, VR, Vetenskapsrådet; Funding text: This research was supported by the European Research Council (grant no. 258980) and the Swedish Research Council (grant no. 2014-4505). The simulations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC 2016/1-562, SNIC 2016/10-47, and 2017/11-25) at the PDC Centre for High Performance Computing (PDC-HPC) and the High Performance Computing Center North (HPC2N). QC 20181022

Available from: 2018-10-22 Created: 2018-10-22 Last updated: 2020-03-09Bibliographically approved

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Lidmar, JackHess, Berk

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