Augmenting Monte Carlo simulations of statistical systems with autoregressive neural networks

Speaker: Prof. UJ dr hab. Piotr Korcyl (Institute of Theoretical Physics, Jagiellonian University, CV: https://ztc.ift.uj.edu.pl/sklad/piotr_korcyl)

Abstract: Markov Chain Monte Carlo simulations have long provided many valuable insights into the dynamics of statistical systems. Most of them have been based on variants of Metropolis-Hastings or cluster algorithms. In the last years, we have observed the emergence of a new class of algorithms based on machine learning techniques. They promise not only to alleviate the critical slowing down phenomenon but also to provide access to thermodynamic observables such as free energy or entropy. It has also been shown recently that information-theoretic measures of correlations such as mutual information can be accessed using such extended algorithms. In the talk, I will explain in what capacity neural networks can be used in Monte Carlo simulations and I will discuss the possible benefits and the limitations. I will illustrate the main points with our results obtained for simple statistical systems such as the Ising and Potts models. I will also briefly describe the state-of-the-art status and future prospects of neural network-enhanced algorithms for statistical systems and lattice field theory.

References:[1] P. Bialas, C. Vaibhav, P. Korcyl, T. Stebel, M. Winiarski, D. Zapolski, [arxiv:2503.08610 [cond-mat.statmech]] (2025) [2] P. Bialas, P. Korcyl, T. Stebel, D. Zapolski, Phys. Rev. E 110, no. 4, 044116 (2024) [3] P. Bialas, P. Korcyl and T. Stebel,  Phys.Rev.E 108, no. 4, 4 (2023) [4] P. Bialas, P. Czarnota, P. Korcyl and T. Stebel, Phys. Rev. E 107, no.5, 054127 (2023)[5] P. Bialas, P. Korcyl and T. Stebel, Comput. Phys. Commun. 281, 108502 (2022).[6] P. Bialas, P. Korcyl and T. Stebel, Phys. Rev. E 107, no.1, 015303 (2023) 

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