TY - JOUR

T1 - Dynamical Computation of the Density of States and Bayes Factors Using Nonequilibrium Importance Sampling

AU - Rotskoff, Grant M.

AU - Vanden-Eijnden, Eric

N1 - Funding Information:
The authors thank Daan Frenkel, Stefano Martiniani, K. Julian Schrenk, and Shang-Wei Ye for discussions that helped motivate this work. G. M. R. acknowledges support from the James S. McDonnell Foundation. E. V. E. was supported by National Science Foundation (NSF) Materials Research Science and Engineering Center Program Grant No. DMR-1420073 and by NSF Grant No. DMS-1522767.
Publisher Copyright:
© 2019 American Physical Society.

PY - 2019/4/16

Y1 - 2019/4/16

N2 - Nonequilibrium sampling is potentially much more versatile than its equilibrium counterpart, but it comes with challenges because the invariant distribution is not typically known when the dynamics breaks detailed balance. Here, we derive a generic importance sampling technique that leverages the statistical power of configurations transported by nonequilibrium trajectories and can be used to compute averages with respect to arbitrary target distributions. As a dissipative reweighting scheme, the method can be viewed in relation to the annealed importance sampling (AIS) method and the related Jarzynski equality. Unlike AIS, our approach gives an unbiased estimator, with a provably lower variance than directly estimating the average of an observable. We also establish a direct relation between a dynamical quantity, the dissipation, and the volume of phase space, from which we can compute quantities such as the density of states and Bayes factors. We illustrate the properties of estimators relying on this sampling technique in the context of density of state calculations, showing that it scales favorable with dimensionality - in particular, we show that it can be used to compute the phase diagram of the mean-field Ising model from a single nonequilibrium trajectory. We also demonstrate the robustness and efficiency of the approach with an application to a Bayesian model comparison problem of the type encountered in astrophysics and machine learning.

AB - Nonequilibrium sampling is potentially much more versatile than its equilibrium counterpart, but it comes with challenges because the invariant distribution is not typically known when the dynamics breaks detailed balance. Here, we derive a generic importance sampling technique that leverages the statistical power of configurations transported by nonequilibrium trajectories and can be used to compute averages with respect to arbitrary target distributions. As a dissipative reweighting scheme, the method can be viewed in relation to the annealed importance sampling (AIS) method and the related Jarzynski equality. Unlike AIS, our approach gives an unbiased estimator, with a provably lower variance than directly estimating the average of an observable. We also establish a direct relation between a dynamical quantity, the dissipation, and the volume of phase space, from which we can compute quantities such as the density of states and Bayes factors. We illustrate the properties of estimators relying on this sampling technique in the context of density of state calculations, showing that it scales favorable with dimensionality - in particular, we show that it can be used to compute the phase diagram of the mean-field Ising model from a single nonequilibrium trajectory. We also demonstrate the robustness and efficiency of the approach with an application to a Bayesian model comparison problem of the type encountered in astrophysics and machine learning.

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U2 - 10.1103/PhysRevLett.122.150602

DO - 10.1103/PhysRevLett.122.150602

M3 - Article

C2 - 31050526

AN - SCOPUS:85064844240

SN - 0031-9007

VL - 122

JO - Physical Review Letters

JF - Physical Review Letters

IS - 15

M1 - 150602

ER -