Bayesian Umbrella Quadrature Automates Free-Energy Calculations Across Diverse Molecular Systems and Processes

Biased sampling in molecular dynamics simulations overcomes time scale limitations and delivers free-energy landscapes, essential to understand complex atomistic phenomena. However, when applied across diverse systems and processes, biasing protocols often require time- and resource-consuming fine-tuning. In search of robustness, we automate a prominent biasing method, Umbrella Sampling, by leveraging the Umbrella Integration formalism for free-energy calculation. To estimate the value of an integral, i.e., the free energy, our Bayesian Umbrella Quadrature (BUQ) method iteratively selects gradient samples, i.e., bias locations, that most reduce the posterior integral variance based on a noise-tolerant Gaussian process model, which also effectively interpolates between samples. We validate the method for a conformational change in a small peptide, a water-to-ice phase transition, and a substitution chemical reaction; demonstrating that BUQ provides an automated free-energy calculation framework that is accurate and robust across fundamentally different systems and processes. To ease adoption, we interface BUQ with widespread simulation packages and share hyperparametrization guidelines.