Using physical property surrogate models to perform accelerated multi-fidelity optimization of force field parameters

Accurate representations of van der Waals dispersion–repulsion interactions play an important role in high-quality molecular dynamics simulations. Training the force field parameters used in the Lennard Jones (LJ) potential typically used to represent these interactions is challenging, generally requiring adjustment based on simulations of macroscopic physical properties. The large computational expense of these simulations, especially when many parameters must be trained simultaneously, limits the size of training data set and number of optimization steps that can be taken, often requiring modelers to perform optimizations within a local parameter region. To allow for more global LJ parameter optimization against large training sets, we introduce a multi-fidelity optimization technique which uses Gaussian process surrogate modeling to build inexpensive models of physical properties as a function of LJ parameters. This approach allows for fast evaluation of approximate objective functions, greatly accelerating searches over parameter space and enabling the use of optimization algorithms capable of searching more globally. In this study, we use an iterative framework which performs global optimization with differential evolution at the surrogate level, followed by validation at the simulation level and surrogate refinement. Using this technique on two previously studied training sets, containing up to 195 physical property targets, we refit a subset of the LJ parameters for the OpenFF 1.0.0 (Parsley) force field. We demonstrate that this multi-fidelity technique can find improved parameter sets compared to a purely simulation-based optimization by searching more broadly and escaping local minima. Additionally, this technique often finds significantly different parameter minima that have comparably accurate performance. In most cases, these parameter sets are transferable to other similar molecules in a test set. Our multi-fidelity technique provides a platform for rapid, more global optimization of molecular models against physical properties, as well as a number of opportunities for further refinement of the technique.

and , for OpenFF 1.0.0, simulation-only refit parameters, and retrained parameters from =5 initial points multi-fidelity run 1. Error bars represent bootstrapped 95% confidence intervals and , for OpenFF 1.0.0, simulation-only refit parameters, and retrained parameters from =5 initial points multi-fidelity run 2. Error bars represent bootstrapped 95% confidence intervals and , for OpenFF 1.0.0, simulation-only refit parameters, and retrained parameters from =5 initial points multi-fidelity run 3. Error bars represent bootstrapped 95% confidence intervals and , for OpenFF 1.0.0, simulation-only refit parameters, and retrained parameters from =5 initial points multi-fidelity run 4. Error bars represent bootstrapped 95% confidence intervals Figure 10. Bias in training set Δ and , as measured by the mean signed deviation (MSD), for OpenFF 1.0.0, simulation-only refit, and retrained parameters from =5 multi-fidelity run 4. Error bars represent bootstrapped 95% confidence intervals 2.1.5 Run 5 Figure 11. RMSE in training set Δ and , for OpenFF 1.0.0, simulation-only refit parameters, and retrained parameters from =5 initial points multi-fidelity run 5. Error bars represent bootstrapped 95% confidence intervals and , as measured by the mean signed deviation (MSD), for OpenFF 1.0.0, simulation-only refit, and retrained parameters from =5 multi-fidelity run 5. Error bars represent bootstrapped 95% confidence intervals 2.2 "Pure only" optimization, =10 2.2.1 Run 1 Figure 13. RMSE in training set Δ and , for OpenFF 1.0.0, simulation-only refit parameters, and retrained parameters from =10 initial points multi-fidelity run 1. Error bars represent bootstrapped 95% confidence intervals         and ( ), as measured by the mean signed deviation (MSD), for OpenFF 1.0.0 and retrained parameters from =20 multi-fidelity optimization against "mixture-only" training set. Error bars represent bootstrapped 95% confidence intervals Figure 33. Per-moiety training set RMSE at each accepted optimization step, for =20 multi-fidelity optimization against "mixture-only" training set.

Test set performance
3.1 "Pure only", N=10 3.1.1 Run 1 Figure 34. Benchmark RMSE over the four types of physical property data in the test set, split by function group or functional group mixture. RMSEs plotted for OpenFF 1.0.0 (gray), multi-fidelity N=10 run 1 against the "pure only" training set (blue), and the simulation-only optimization against the same training set (brown). Error bars represent 95% confidence intervals, bootstrapped over the properties in the dataset. Figure 35. Benchmark RMSE over the four types of physical property data in the test set, split by function group or functional group mixture. RMSEs plotted for OpenFF 1.0.0 (gray), multi-fidelity N=10 run 2 against the "pure only" training set (orange), and the simulation-only optimization against the same training set (brown). Error bars represent 95% confidence intervals, bootstrapped over the properties in the dataset.

Run 3
Figure 36. Benchmark RMSE over the four types of physical property data in the test set, split by function group or functional group mixture. RMSEs plotted for OpenFF 1.0.0 (gray), multi-fidelity N=10 run 3 against the "pure only" training set (green), and the simulation-only optimization against the same training set (brown). Error bars represent 95% confidence intervals, bootstrapped over the properties in the dataset.

Run 4
Figure 37. Benchmark RMSE over the four types of physical property data in the test set, split by function group or functional group mixture. RMSEs plotted for OpenFF 1.0.0 (gray), multi-fidelity N=10 run 4 against the "pure only" training set (red), and the simulation-only optimization against the same training set (brown). Error bars represent 95% confidence intervals, bootstrapped over the properties in the dataset.
3.1.5 Run 5 Figure 38. Benchmark RMSE over the four types of physical property data in the test set, split by function group or functional group mixture. RMSEs plotted for OpenFF 1.0.0 (gray), multi-fidelity N=10 run 5 against the "pure only" training set (purple), and the simulation-only optimization against the same training set (brown). Error bars represent 95% confidence intervals, bootstrapped over the properties in the dataset.

"Mixture only", N=10
Figure 39. Benchmark RMSE over the four types of physical property data in the test set, split by function group or functional group mixture. RMSEs plotted for OpenFF 1.0.0 (gray), multi-fidelity N=10 run against the "mixture only" training set (blue), and the simulation-only optimization against the same training set (brown). Error bars represent 95% confidence intervals, bootstrapped over the properties in the dataset.

"Mixture only", N=20
Figure 40. Benchmark RMSE over the four types of physical property data in the test set, split by function group or functional group mixture. RMSEs plotted for OpenFF 1.0.0 (gray), multi-fidelity N=20 run against the "mixture only" training set (blue), and the simulation-only optimization against the same training set (brown). Error bars represent 95% confidence intervals, bootstrapped over the properties in the dataset.