Asymptotically unbiased estimation of physical observables with neural samplers.

By K. Nicoli, Shinichi Nakajima, Nils Strodthoff, Wojciech Samek, K. Müller, Pan Kessel. 2020

136 citations recorded by the source corpus.

We propose a general framework for the estimation of observables with generative neural samplers focusing on modern deep generative neural networks that provide an exact sampling probability. In this framework, we present asymptotically unbiased estimators for generic observables, including those that explicitly depend on the partition function such as free energy or entropy, and derive corresponding variance estimators. We demonstrate their practical applicability by numerical experiments for the two-dimensional Ising model which highlight the superiority over existing methods. Our approach greatly enhances the applicability of generative neural samplers to real-world physical systems.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics, Probabilistic & Bayesian Methods

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Citations in the corpus

Stochastic Normalizing Flows (2020, methodology): “…ﬂows with importance sampling methods to Boltzmann Generators (No ´ e et al., 2019), an approach now popular in molecular and material sciences and nuclear physics (M¨uller et al., 2018; Li & Wang, 2018; No ´ e et al., 2019; K ¨ ohler et al., 2019; Albergo et al., 2019; Nicoli et al., 2019).”
Equivariant Flows: exact likelihood generative learning for symmetric densities (2020, background): “Copyright 2020 by the author(s). approach is widely applicable in the physical sciences, and has also been employed in the sampling of spin lattice states (Nicoli et al., 2019; Li & Wang, 2018) and nuclear physics models (Albergo et al., 2019).”