Advanced simulation algorithms for amorphous materials: from enhanced sampling to structural optimisation

Understanding the structure and dynamics of amorphous materials remains one of the major challenges in statistical physics. These difficulties stem from the complexity of their configurational landscapes, which gives rise to collective phenomena and extremely slow dynamics. In recent years, advances in machine learning and non-equilibrium algorithms have provided promising tools to tackle these challenges. In this thesis, we contribute to this growing effort by developing a set of algorithmic strategies to enhance sampling of complex landscapes and to optimise selected structural properties. We begin by introducing a general framework for adaptive Monte Carlo sampling inspired by policy gradient methods in reinforcement learning. This Policy-guided Monte Carlo approach dynamically adjusts the proposal distribution in the Metropolis–Hastings algorithm to maximise sampling efficiency. We demonstrate its application to paradigmatic models of glass-forming mixtures, where it can accelerate convergence in specific cases. We then explore a more expressive, though less general, approach to sampling built upon flow-based generative models. In particular, we extend the recent stochastic interpolants framework to particle systems, adapting it to their geometric constraints and underlying symmetries. We assess the limitations of current architectures in generating accurate samples for representative models of complex fluids. Moving beyond equilibrium sampling, we employ non-equilibrium algorithms to optimise targeted structural properties of disordered solids. Specifically, we generate hyperuniform configurations and samples exhibiting a high degree of local order. We then assess the stability of these configurations and find that neither feature correlates with better glasses, challenging recent claims in the literature. We believe this work offers a new set of advanced algorithmic tools to tackle key computational challenges related to the high-dimensional landscapes of disordered and complex systems.