Automated optimization of force field parameters against ensemble-averaged measurements with Bayesian inference of conformational populations.

Accurate force fields are essential for reliable molecular simulations. These models are refined against quantum mechanical calculations and experimental measurements, which are subject to random and systematic errors. Bayesian Inference of Conformational Populations (BICePs) is a reweighting algorithm that reconciles simulated ensembles with sparse or noisy observables by sampling the full posterior distribution of conformational populations and experimental uncertainty. In this method, a metric called the BICePs score is used to perform model selection by calculating the free energy of "turning on" the conformational populations under experimental restraints. This approach, when used with improved likelihood functions to deal with experimental outliers, can be used for force field validation [R. M. Raddi, T. Marshall, Y. Ge, and V. A. Voelz, J. Chem. Theory Comput. 21, 5880 (2025)]. Here, we extend the BICePs approach to perform automated force field refinement while simultaneously sampling the full distribution of uncertainties, using a variational method to minimize the BICePs score. To demonstrate the utility of this method, we refine multiple interaction parameters for a 12-mer HP lattice model using ensemble-averaged distance measurements as restraints. To illustrate the resilience of BICePs in the presence of unknown random and systematic errors, we assess the performance of our algorithm through repeated optimizations and under various extents of experimental error. Our results suggest that variational optimization of the BICePs score is a promising direction for robust and automatic parameterization of molecular potentials.