Piotr Bialas

Piotr Bialas, Piotr Korcyl, Tomasz Stebel

Machine learning techniques, in particular the so-called normalizing flows, are becoming increasingly popular in the context of Monte Carlo simulations as they can effectively approximate target probability distributions. In the case of lattice field theories (LFT) the target distribution is given by the exponential of the action. The common loss function's gradient estimator based on the "reparametrization trick" requires the calculation of the derivative of the action with respect to the fields. This can present a significant computational cost for complicated, non-local actions like e.g. fermionic action in QCD. In this contribution, we propose an estimator for normalizing flows based on the REINFORCE algorithm that avoids this issue. We apply it to two dimensional Schwinger model with Wilson fermions at criticality and show that it is up to ten times faster in terms of the wall-clock time as well as requiring up to $30\%$ less memory than the reparameterization trick estimator. It is also more numerically stable allowing for single precision calculations and the use of half-float tensor cores. We present an in-depth analysis of the origins of those improvements. We believe that these benefits will appear also outside the realm of the LFT, in each case where the target probability distribution is computationally intensive.

Piotr Bialas, Piotr Korcyl, Tomasz Stebel et al.

We present the \texttt{NeuMC} software package, based on \pytorch, aimed at facilitating the research on neural samplers in lattice field theories. Neural samplers based on normalizing flows are becoming increasingly popular in the context of Monte-Carlo simulations as they can effectively approximate target probability distributions, possibly alleviating some shortcomings of the Markov chain Monte-Carlo methods. Our package provides tools to create such samplers for two-dimensional field theories.

Piotr Bialas, Piotr Korcyl, Tomasz Stebel

Recently a machine learning approach to Monte-Carlo simulations called Neural Markov Chain Monte-Carlo (NMCMC) is gaining traction. In its most popular form it uses neural networks to construct normalizing flows which are then trained to approximate the desired target distribution. In this contribution we present new gradient estimator for Stochastic Gradient Descent algorithm (and the corresponding \texttt{PyTorch} implementation) and show that it leads to better training results for $φ^4$ model. For this model our estimator achieves the same precision in approximately half of the time needed in standard approach and ultimately provides better estimates of the free energy. We attribute this effect to the lower variance of the new estimator. In contrary to the standard learning algorithm our approach does not require estimation of the action gradient with respect to the fields, thus has potential of further speeding up the training for models with more complicated actions.