Neural networks-based variationally enhanced sampling

Authors: Luigi Bonati1*, Yue-Yu Zhang2, Michele Parrinello2

  1. Department of Physics, ETH Zurich, 8092 Zurich, Switzerland and Facoltà di Informatica, Instituto di Scienze Computazionali, Università della Svizzera italiana, 6900 Lugano, Switzerland
  2. Department of Chemistry and Applied Biosciences, ETH Zurich, 8092 Zurich, Switzerland and Facoltà di Informatica, Instituto di Scienze Computazionali, Università della Svizzera italiana (USI), 6900 Lugano, Switzerland
  • Corresponding author email:

DOI10.24435/materialscloud:2019.0065/v1 (version v1, submitted on 22 October 2019)

How to cite this entry

Luigi Bonati, Yue-Yu Zhang, Michele Parrinello, Neural networks-based variationally enhanced sampling, Materials Cloud Archive (2019), doi: 10.24435/materialscloud:2019.0065/v1.


Sampling complex free-energy surfaces is one of the main challenges of modern atomistic simulation methods. The presence of kinetic bottlenecks in such surfaces often renders a direct approach useless. A popular strategy is to identify a small number of key collective variables and to introduce a bias potential that is able to favor their fluctuations in order to accelerate sampling. Here, we propose to use machine-learning techniques in conjunction with the recent variationally enhanced sampling method [O. Valsson, M. Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] in order to determine such potential. This is achieved by expressing the bias as a neural network. The parameters are determined in a variational learning scheme aimed at minimizing an appropriate functional. This required the development of a more efficient minimization technique. The expressivity of neural networks allows representing rapidly varying free-energy surfaces, removes boundary effects artifacts, and allows several collective variables to be handled.

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External references

Journal reference
L. Bonati, Y.-Y. Zhang, M. Parrinello, Proceedings of the National Academy of Sciences, 116(36), 17641–17647 (2019) doi:10.1073/pnas.1907975116


MARVEL MARVEL/DD1 enhanced-sampling deep-learning PLUMED biomolecules silicon crystallization rare-events

Version history

22 October 2019 [This version]