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Nonequilibrium sampling is potentially much more versatile than itsequilibrium counterpart, but it comes with challenges because the invariantdistribution is not typically known when the dynamics breaks detailed balance.Here, we derive a generic importance sampling technique that leverages thestatistical power of configurations transported by nonequilibrium trajectories,and can be used to compute averages with respect to arbitrary targetdistributions. As a dissipative reweighting scheme, the method can be viewed inrelation to the annealed importance sampling (AIS) method and the relatedJarzynski equality. Unlike AIS, our approach gives an unbiased estimator, withprovably lower variance than directly estimating the average of an observable.We also establish a direct relation between a dynamical quantity, thedissipation, and the volume of phase space, from which we can computequantities such as the density of states and Bayes factors. We illustrate theproperties of estimators relying on this sampling technique in the context ofdensity of state calculations, showing that it scales favorable withdimensionality -- in particular, we show that it can be used to compute thephase diagram of the mean-field Ising model from a single nonequilibriumtrajectory. We also demonstrate the robustness and efficiency of the approachwith an application to a Bayesian model comparison problem of the typeencountered in astrophysics and machine learning.

Dynamical computation of the density of states and Bayes factors using nonequilibrium importance sampling