Integration of Deep Learning Methods and Monte Carlo Techniques for Estimating Molecular Observables (2024)
In this thesis, we introduce ab-flowMC, an adaptive Markov chain Monte Carlo (MCMC) framework that enables the simultaneous training of one Normalizing Flow (NF) and one Machine Learning Potential (MLP) per state while sampling a Boltzmann weighted molecular ensemble. This approach allows for the rapid convergence of the system towards the Boltzmann distribution. For each isomer of a molecular system, ab-flowMC actively trains an NF to propose reliable configurations and an MLP to predict energies, using an adaptive MCMC. This methodology enables the simultaneous learning of surrogate models for both the configuration distribution and the energies, with active improvement in regions of interest as indicated by the MCMC. After convergence, the trained NFs and MLPs facilitate fast and accurate computations of important thermodynamic observables, such as optical spectra and free-energy differences. Ab-flowMC uses Density Functional Theory (DFT) to keep the quantum-mechanical accuracy in the energy predictions and sampling processes. Moreover, the NFs and MLPs trained for each isomer are combined into a mixture model, which serves as a proposal distribution in a Metropolis-Hastings MCMC algorithm. This mixture model significantly enhances the efficiency of sampling across different states, achieving a non-local exploration. Finally, to demonstrate the effectiveness of the ab-flowMC framework, we applied it to study the Ag6 nanocluster, which exhibits two distinct isomers. The method allowed us to accurately compute the optical spectra, calculate the free-energy difference between the two isomers, and determine the populations of each one of them.