Asymptotically unbiased estimation of physical observables with neural samplers

Kim A Nicoli; Shinichi Nakajima; Nils Strodthoff; Wojciech Samek; Klaus-Robert Müller; Pan Kessel

doi:10.1103/PhysRevE.101.023304

Asymptotically unbiased estimation of physical observables with neural samplers

Phys Rev E. 2020 Feb;101(2-1):023304. doi: 10.1103/PhysRevE.101.023304.

Authors

Kim A Nicoli¹, Shinichi Nakajima², Nils Strodthoff³, Wojciech Samek⁴, Klaus-Robert Müller⁵, Pan Kessel⁶

Affiliations

¹ Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany.
² Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany; Berlin Big Data Center, 10587 Berlin, Germany; and RIKEN Center for AIP, 103-0027, Tokyo, Japan.
³ Fraunhofer Heinrich Hertz Institute, 10587 Berlin, Germany.
⁴ Fraunhofer Heinrich Hertz Institute, 10587 Berlin, Germany; Berlin Big Data Center, 10587 Berlin, Germany; and Berliner Zentrum für Maschinelles Lernen, 10587 Berlin, Germany.
⁵ Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany; Berlin Big Data Center, 10587 Berlin, Germany; Department of Brain and Cognitive Engineering, Korea University, Anam-dong, Seongbuk-gu, Seoul 136-713, South Korea; Max-Panck-Institut für Informatik, 66123 Saarbrücken, Germany; and Berliner Zentrum für Maschinelles Lernen, 10587 Berlin, Germany.
⁶ Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany and Berlin Big Data Center, 10587 Berlin, Germany.

PMID: 32168605
DOI: 10.1103/PhysRevE.101.023304

Abstract

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.