  We explore a self-learning Markov chain Monte Carlo method based on the
Adversarial Non-linear Independent Components Estimation Monte Carlo, which
utilizes generative models and artificial neural networks. We apply this method
to the scalar $\varphi^4$ lattice field theory in the weak-coupling regime and,
in doing so, greatly increase the system sizes explored to date with this
self-learning technique. Our approach does not rely on a pre-existing training
set of samples, as the agent systematically improves its performance by
bootstrapping samples collected by the model itself. We evaluate the
performance of the trained model by examining its mixing time and study the
ergodicity of generated samples. When compared to methods such as Hamiltonian
Monte Carlo, this approach provides unique advantages such as the speed of
inference and a compressed representation of Monte Carlo proposals for
potential use in downstream tasks.

Disordered Systems and Neural Networks;Statistical Mechanics;Computational Physics