Fast and Sample-Efficient Interatomic Neural Network Potentials for Molecules and Materials Based on Gaussian Moments

Abstract

Artificial neural networks (NNs) are one of the most frequently used machine learning approaches to construct interatomic potentials and enable efficient large-scale atomistic simulations with almost ab initio accuracy. However, the simultaneous training of NNs on energies and forces, which are a prerequisite for, e.g., molecular dynamics simulations, can be demanding. In this work, we present an improved NN architecture based on the previous GM-NN model [J. Chem. Theory Comput20201654105421], which shows an improved prediction accuracy and considerably reduced training times. Moreover, we extend the applicability of Gaussian moment-based interatomic potentials to periodic systems and demonstrate the overall excellent transferability and robustness of the respective models. The fast training by the improved methodology is a prerequisite for training-heavy workflows such as active learning or learning-on-the-fly.

Exploring chemical and conformational spaces by batch mode deep active learning

“…where c is defined as the root-mean-square error (RMSE) per atom of the mean atomic energy and µ Z i are initialized by solving a linear regression problem. 48 The trainable scale and shift parameters of the atomic energy, i.e. σ Z i and µ Z i , are considered fixed for BMDAL algorithms, similar to β .…”

“…For the QM9 data set, we used a cutoff radius of r max = 3.0 Å. 47,48 The application of BMDAL methods to QM9 can be seen as an application to the sampling of the chemical space. Fig.…”

“…For both data sets we used a cutoff radius of r max = 6.5 Å. 48 For the TiO 2 data set, we reserved 6000 structures for the pool data. Depending on the specific scenario, the initial training set contained 10 or 500 structures.…”

“…Defining the radial and angular components of pair distances as r ij = ‖ r ij ‖ 2 and r̂ ij = r ij /r ij , features equivariant to rotations can be obtained as 47,48 where is the L -fold outer product of the angular components and R Z i , Z j , s ( r ij , β ) are nonlinear radial functions with trainable parameters β . We employ a weighted sum of Gaussian functions as nonlinear radial functions, 48 rescaled by the cosine cutoff function. 49 Features invariant to rotations are recovered by computing tensor contractions of Cartesian tensors Ψ i , L , s .…”

“…We employ a fully-connected feed-forward NN consisting of two hidden layers 48 with d 0 = 360 being the number of input neurons, d 1 = d 2 = 512 being the number of hidden neurons, and the single output neuron d 3 = 1. Moreover, we employ the neural tangent kernel (NTK) parameterization, 32 i.e.…”