Abstract:

Metropolis Monte Carlo (MMC) simulations are a foundational method in computational chemistry for exploring the configurational space of manybody systems. Despite their utility, a key limitation of traditional MMC is the slow sampling rate, particularly in high-dimensional or complex systems, leading to inefficient sampling and high computational cost. This study investigates whether machine learning can enhance the efficiency of MMC by improving the acceptance rate of proposed configurations.

To explore this, I implemented two separate MMC simulations of a simple, two particle Lennard Jones system. The baseline method uses conventional random-walk proposals, where proposed configurations are generated as small perturbations of previously accepted ones. In contrast, the ML-aided approach leverages a normalizing flow, a generative ML model, trained on configurations obtained from an initial MMC run. This model then proposes uncorrelated configurations by sampling from its learned distribution, aimed at improving sampling efficiency.

Contrary to expectations, the ML-guided proposals resulted in a lower acceptance rate than the traditional approach. Preliminary analysis suggests this may be due to insufficient overlap between the ML model’s learned distribution and the true Boltzmann distribution, leading to proposals that are not accepted despite being “likely” under the ML model.

These results suggest that while machine learning has promise in enhancing Monte Carlo methods, naïvely replacing proposal mechanisms with ML-based models may not yield immediate benefits. Future work will explore improved training strategies, such as incorporating potential energy calculations to better align the learned and target distributions. This study provides insight into the challenges of integrating ML into classical simulation workflows and highlights the need for careful model validation to ensure physical relevance.

Speaker:

Enoch Woldu, University of Chicago

Enoch Woldu is a third year math and physics student at the University of Chicago. He is currently working at a computational research lab at the University of Chicago where he has spent the past year using machine learning to more effectively learn the Boltzmann Distribution of various systems.