Gaussian Moments as Physically Inspired Molecular Descriptors for Accurate and Scalable Machine Learning Potentials

Abstract

Machine learning techniques allow a direct mapping of atomic positions and nuclear charges to the potential energy surface with almost ab-initio accuracy and the computational efficiency of empirical potentials. In this work we propose a machine learning method for constructing highdimensional potential energy surfaces based on feed-forward neural networks. As input to the neural network we propose an extendable invariant local molecular descriptor constructed from geometric moments. Their formulation via pairwise distance vectors and tensor contractions allows a very efficient implementation on graphical processing units (GPUs). The atomic species is encoded in the molecular descriptor, which allows the restriction to one neural network for the training of all atomic species in the data set. We demonstrate that the accuracy of the developed approach in representing both chemical and configurational spaces is comparable to the one of several established machine learning models. Due to its high accuracy and efficiency, the proposed machine-learned potentials can be used for any further tasks, for example the optimization of molecular geometries, the calculation of rate constants or molecular dynamics.

Choosing the right molecular machine learning potential

“…43,48 The list of developed LDs for molecules is extensive. It includes, among others, BP-ACSFs (Behler-Parrinello's atom-centered symmetry functions) 70 and its ANI-AEV (atomic environment vectors) 46 and wACSF (weighted ACSF) modifications, 71 SOAP (smooth overlap of atomic positions), 43 aSLATM (atomic Spectrum of London and Axilrod-Teller-Muto), 45 FCHL (Faber-Christensen-Huang-Lilienfeld), 44 Gaussian moments, 72 spherical Bessel functions, 73,74 and descriptors used in DPMD (deep potential molecular dynamics) 47 and DeepPot-SE (DPMD-smooth edition). 75 Local descriptors can be fixed before training an MLP.…”

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

“…The results in Table 5 show that the linear ACE model performs significantly better than GAP, achieving errors in the same ballpark as the other methods for the unknown molecules, but using orders of magnitudes less training data. In particular, the ACE model matches the energy error of the state of the art GM-sNN 19 on the unknown molecules, demonstrating its excellent extrapolation capabilities. For all the neural network models, the error on known molecules is quite a bit lower than that for the unknown molecules, which we consider to be a sign of overfitting.…”

“…Molecular mechanics (e.g. AMBER, 2 CHARMM 12 and OPLS 13 ), machine learning: Kernels (GAP, 14 FCHL 15 and sGDML16 ), Neural Networks (ANI,17 PaiNN,18 GMsNN,19 DimeNet,20 Cormorant, 21 Schnet 22 and Physnet23 ).…”

“…MAE of energy (E, meV) and force (F, meV/Å) predictions of models recently published that were trained on 50,000 geometries of the original MD17 data set. 21 Schnet 22 Physnet 23 GMdNN19…”

Analytical gradients for molecular-orbital-based machine learning

“…14 The ISO17 data set consists of conformers taken from MD trajectories for constitutional isomers with the chemical formula C 7 O 2 H 10 . Table II shows the performance of two MOB-ML models, one trained on 220 QM7b-T structures and one trained on 100 ISO17 structures, and summarizes the MAEs obtained with other ML models in the literature, i.e., SchNet, 14 FCHL, 21 PhysNet, 22 the shared-weight neural network (SWNN), 23 GM-sNN, 25 and GNNFF. 26 The MOB-ML models are the only ML models which are on average chemically accurate although the MOB-ML models were only trained on energies for 100 ISO17 molecules and 220 QM7b-T molecules, respectively.…”