Path-space variational inference for non-equilibrium coarse-grained systems

Vagelis Harmandaris, Evangelia Kalligiannaki*, Markos Katsoulakis, Petr Plecháč

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


In this paper we discuss information-theoretic tools for obtaining optimized coarse-grained molecular models for both equilibrium and non-equilibrium molecular simulations. The latter are ubiquitous in physicochemical and biological applications, where they are typically associated with coupling mechanisms, multi-physics and/or boundary conditions. In general the non-equilibrium steady states are not known explicitly as they do not necessarily have a Gibbs structure.The presented approach can compare microscopic behavior of molecular systems to parametric and non-parametric coarse-grained models using the relative entropy between distributions on the path space and setting up a corresponding path-space variational inference problem. The methods can become entirely data-driven when the microscopic dynamics are replaced with corresponding correlated data in the form of time series. Furthermore, we present connections and generalizations of force matching methods in coarse-graining with path-space information methods. We demonstrate the enhanced transferability of information-based parameterizations to different observables, at a specific thermodynamic point, due to information inequalities.We discuss methodological connections between information-based coarse-graining of molecular systems and variational inference methods primarily developed in the machine learning community. However, we note that the work presented here addresses variational inference for correlated time series due to the focus on dynamics. The applicability of the proposed methods is demonstrated on high-dimensional stochastic processes given by overdamped and driven Langevin dynamics of interacting particles.

Original languageEnglish (US)
Pages (from-to)355-383
Number of pages29
JournalJournal of Computational Physics
StatePublished - Jun 1 2016

Bibliographical note

Funding Information:
The research of E.K. and V.H. was supported by European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF), under the THALES Program, grant AMOSICSS . The research of V.H. was also partially supported by ARISTEIA II, grant MULTI-MODEL-COMPLEX . The research of M.K. was partially supported by the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract No. DE-SC0010723 and the National Science Foundation under Grant No. DMS 1515172 . The research of P.P. was partially supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-SC-0007046 .

Publisher Copyright:
© 2016 Elsevier Inc.


  • Coarse graining
  • Information metrics
  • Langevin dynamics
  • Machine learning
  • Non-equilibrium
  • Stochastic optimization
  • Time series
  • Variational inference

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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