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Title: Wavelets as basis functions to represent the coarse-graining potential in multiscale coarse graining approach

Abstract

In this paper, we apply Multiresolution Analysis (MRA) to develop sparse but accurate representations for the Multiscale Coarse-Graining (MSCG) approximation to the many-body potential of mean force. We rigorously framed the MSCG method into MRA so that all the instruments of this theory become available together with a multitude of new basis functions, namely the wavelets. The coarse-grained (CG) force field is hierarchically decomposed at different resolution levels enabling to choose the most appropriate wavelet family for each physical interaction without requiring an a priori knowledge of the details localization. The representation of the CG potential in this new efficient orthonormal basis leads to a compression of the signal information in few large expansion coefficients. The multiresolution property of the wavelet transform allows to isolate and remove the noise from the CG force-field reconstruction by thresholding the basis function coefficients from each frequency band independently. We discuss the implementation of our wavelet-based MSCG approach and demonstrate its accuracy using two different condensed-phase systems, i.e. liquid water and methanol. Simulations of liquid argon have also been performed using a one-to-one mapping between atomistic and CG sites. The latter model allows to verify the accuracy of the method and to test differentmore » choices of wavelet families. Furthermore, the results of the computer simulations show that the efficiency and sparsity of the representation of the CG force field can be traced back to the mathematical properties of the chosen family of wavelets. This result is in agreement with what is known from the theory of multiresolution analysis of signals.« less

Authors:
 [1];  [2];  [1];  [3];  [1]
  1. SUPSI, Department of Innovative Technology, Galleria 2, 6928 Manno (Switzerland)
  2. (Switzerland)
  3. USI, Institute of Computational Science, Via Buffi 13, 6906 Lugano (Switzerland)
Publication Date:
OSTI Identifier:
22570189
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 300; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; APPROXIMATIONS; ARGON; COMPRESSION; COMPUTERIZED SIMULATION; FUNCTIONS; LIQUIDS; MANY-BODY PROBLEM; METHANOL; MOLECULAR DYNAMICS METHOD; NOISE; POTENTIALS; RESOLUTION; SIGNALS; WATER

Citation Formats

Maiolo, M., E-mail: massimo.maiolo@zhaw.ch, ZHAW, Institut für Angewandte Simulation, Grüental, CH-8820 Wädenswil, Vancheri, A., E-mail: alberto.vancheri@supsi.ch, Krause, R., E-mail: rolf.krause@usi.ch, and Danani, A., E-mail: andrea.danani@supsi.ch. Wavelets as basis functions to represent the coarse-graining potential in multiscale coarse graining approach. United States: N. p., 2015. Web. doi:10.1016/J.JCP.2015.07.039.
Maiolo, M., E-mail: massimo.maiolo@zhaw.ch, ZHAW, Institut für Angewandte Simulation, Grüental, CH-8820 Wädenswil, Vancheri, A., E-mail: alberto.vancheri@supsi.ch, Krause, R., E-mail: rolf.krause@usi.ch, & Danani, A., E-mail: andrea.danani@supsi.ch. Wavelets as basis functions to represent the coarse-graining potential in multiscale coarse graining approach. United States. https://doi.org/10.1016/J.JCP.2015.07.039
Maiolo, M., E-mail: massimo.maiolo@zhaw.ch, ZHAW, Institut für Angewandte Simulation, Grüental, CH-8820 Wädenswil, Vancheri, A., E-mail: alberto.vancheri@supsi.ch, Krause, R., E-mail: rolf.krause@usi.ch, and Danani, A., E-mail: andrea.danani@supsi.ch. Sun . "Wavelets as basis functions to represent the coarse-graining potential in multiscale coarse graining approach". United States. https://doi.org/10.1016/J.JCP.2015.07.039.
@article{osti_22570189,
title = {Wavelets as basis functions to represent the coarse-graining potential in multiscale coarse graining approach},
author = {Maiolo, M., E-mail: massimo.maiolo@zhaw.ch and ZHAW, Institut für Angewandte Simulation, Grüental, CH-8820 Wädenswil and Vancheri, A., E-mail: alberto.vancheri@supsi.ch and Krause, R., E-mail: rolf.krause@usi.ch and Danani, A., E-mail: andrea.danani@supsi.ch},
abstractNote = {In this paper, we apply Multiresolution Analysis (MRA) to develop sparse but accurate representations for the Multiscale Coarse-Graining (MSCG) approximation to the many-body potential of mean force. We rigorously framed the MSCG method into MRA so that all the instruments of this theory become available together with a multitude of new basis functions, namely the wavelets. The coarse-grained (CG) force field is hierarchically decomposed at different resolution levels enabling to choose the most appropriate wavelet family for each physical interaction without requiring an a priori knowledge of the details localization. The representation of the CG potential in this new efficient orthonormal basis leads to a compression of the signal information in few large expansion coefficients. The multiresolution property of the wavelet transform allows to isolate and remove the noise from the CG force-field reconstruction by thresholding the basis function coefficients from each frequency band independently. We discuss the implementation of our wavelet-based MSCG approach and demonstrate its accuracy using two different condensed-phase systems, i.e. liquid water and methanol. Simulations of liquid argon have also been performed using a one-to-one mapping between atomistic and CG sites. The latter model allows to verify the accuracy of the method and to test different choices of wavelet families. Furthermore, the results of the computer simulations show that the efficiency and sparsity of the representation of the CG force field can be traced back to the mathematical properties of the chosen family of wavelets. This result is in agreement with what is known from the theory of multiresolution analysis of signals.},
doi = {10.1016/J.JCP.2015.07.039},
url = {https://www.osti.gov/biblio/22570189}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = ,
volume = 300,
place = {United States},
year = {2015},
month = {11}
}