Empirical optimization of molecular simulation force fields by Bayesian inference

The demands on the accuracy of force fields for classical molecular dynamics simulations are steadily growing as larger and more complex systems are studied over longer times. One way to meet these growing demands is to hand over the learning of force fields and their parameters to machines in a systematic (semi)automatic manner. Doing so, we can take full advantage of exascale computing, the increasing availability of experimental data, and advances in quantum mechanical computations and the calculation of experimental observables from molecular ensembles. Here, we discuss and illustrate the challenges one faces in this endeavor and explore a way forward by adapting the Bayesian inference of ensembles (BioEn) method [Hummer and Kofinger, J. Chem. Phys. (2015)] for force field parameterization. In the Bayesian inference of force fields (BioFF) method developed here, the optimization problem is regularized by a simplified prior on the force field parameters and an entropic prior acting on the ensemble. The latter compensates for the unavoidable over simplifications in the parameter prior. We determine optimal force field parameters using an iterative predictor-corrector approach, in which we run simulations, determine the reference ensemble using the weighted histogram analysis method (WHAM), and update the force field according to the BioFF posterior. We illustrate this approach for a simple polymer model, using the distance between two labeled sites as the experimental observable. By systematically resolving force field issues, instead of just reweighting a structural ensemble, the BioFF corrections extend to observables not included in ensemble reweighting. We envision future force field optimization as a formalized, systematic, and (semi)automatic machine-learning effort that incorporates a wide range of data from experiment and high-level quantum chemical calculations, and takes advantage of exascale computing resources.

Automated summary

As the demands for accuracy in classical molecular dynamics simulations increase, one way to meet these demands is to use machines for the learning of force fields and their parameters in a semi-automatic manner. The Bayesian inference method is adapted for force field parameterization, optimizing force field parameters and updating them based on experimental observations and ensemble analysis. By systematically addressing force field issues and incorporating a wide range of data, including experimental and quantum chemical calculations, future force field optimization efforts can be formalized, systematic, and semi-automatic.