Linear Atomic Cluster Expansion Force Fields for Organic Molecules: Beyond RMSE

Abstract

We demonstrate that fast and accurate linear force fields can be built for molecules using the atomic cluster expansion (ACE) framework. The ACE models parametrize the potential energy surface in terms of body-ordered symmetric polynomials making the functional form reminiscent of traditional molecular mechanics force fields. We show that the four- or five-body ACE force fields improve on the accuracy of the empirical force fields by up to a factor of 10, reaching the accuracy typical of recently proposed machine-learning-based approaches. We not only show state of the art accuracy and speed on the widely used MD17 and ISO17 benchmark data sets, but we also go beyond RMSE by comparing a number of ML and empirical force fields to ACE on more important tasks such as normal-mode prediction, high-temperature molecular dynamics, dihedral torsional profile prediction, and even bond breaking. We also demonstrate the smoothness, transferability, and extrapolation capabilities of ACE on a new challenging benchmark data set comprised of a potential energy surface of a flexible druglike molecule.

Permutationally invariant polynomial regression for energies and gradients, using reverse differentiation, achieves orders of magnitude speed-up with high precision compared to other machine learning methods

“…Very recently, the ACE method has been used to fit the ethanol MD17 data set, as well as datasets for other molecules. 36 This method was trained and tested on splits of 1000 configurations each (energies plus gradients). The ACE method achieves an MAE from around 0.1 kcal mol −1 to a low value of 0.03 kcal mol −1 , depend-ing on the values of the hyperparameters in this method.…”

“…This dataset has been used for this purpose for a number of molecules. 25,26,36 Beyond this important utility, one can inquire about the many uses that the PES fits can be put to.…”

“…There are of course caveats to timings, but in this case, all timings were done on the same compute node, an Intel Xeon Gold 6240 2-Processor 24.75M Cache 2.60 GHz. A similar assessment of some of these ML methods was very recently made including the recent Atomic Cluster Expansion (ACE) method 36 using revised MD17 datasets.…”

“…These methods have been described in detail in the two recent assessment papers 26,36 and so we just give a brief description here. In broad terms these methods can be categorized into kernel-based approaches (e.g., GAP-SOAP, sGDML, KREG, pKREG, KRR) and neural network(NN)-based ones.…”

Multilayer atomic cluster expansion for semi-local interactions

“…Thus, for all other molecules we trained 4layer ACE models and the corresponding performance metrics are summarised in Table II (model details are given in Supplementary Materials). The resulting models outperform most of the machine learning potentials [32][33][34] with the exception of the equivariant neural network potentials NequIP 28 . Note that we only compare to models trained on the revised MD17 dataset and Table II shows comparison to the closely related linear ACE model and the best performing model NequIP.…”