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We present a strategy to construct guiding distribution functions (GDFs)based on variance minimization. Auxiliary dynamics via GDFs mitigates theexponential growth of variance as a function of bias in Monte Carlo estimatorsof large deviation functions. The variance minimization technique exploits theexact properties of eigenstates of the tilted operator that defines the biaseddynamics in the nonequilibrium system. We demonstrate our techniques in twoclasses of problems. In the continuum, we show that GDFs can be optimized tostudy interacting driven diffusive systems where the efficiency issystematically improved by incorporating higher correlations into the GDF. Onthe lattice, we use a correlator product state ansatz to study the 1D WASEP. Weshow that with modest resources we can capture the features of thesusceptibility in large systems that marks the phase transition from uniformtransport to a traveling wave state. Our work extends the repertoire of toolsavailable to study nonequilibrium properties in realistic systems.

Constructing Auxiliary Dynamics for Nonequilibrium Stationary States by Variance Minimization