Active Learning A Neural Network Model For Gold Clusters & Bulk From Sparse First Principles Training Data

Abstract

Small metal clusters are of fundamental scientific interest and of tremendous significance in catalysis. These nanoscale clusters display diverse geometries and structural motifs depending on the cluster size; a knowledge of this size-dependent structural motifs and their dynamical evolution has been of longstanding interest. Given the high computational cost of first-principles calculations, molecular modeling and atomistic simulations such as molecular dynamics (MD) has proven to be an important complementary tool to aid this understanding. Classical MD typically employ predefined functional forms which limits their ability to capture such complex size-dependent structural and dynamical transformation. Neural Network (NN) based potentials represent flexible alternatives and in principle, well-trained NN potentials can provide high level of flexibility, transferability and accuracy on-par with the reference model used for training. A major challenge, however, is that NN models are interpolative and requires large quantities (� 10 4 or greater) of training data to ensure that the model adequately samples the energy landscape both near and far-from-equilibrium. A highly desirable goal is minimize the number of training data, especially if the underlying reference model is first-principles based and hence expensive. Here, we introduce an active learning (AL) scheme that trains a NN model on-thefly with minimal amount of first-principles based training data. Our AL workflow is initiated with a sparse training dataset (�1 to 5 data points) and is updated on-the-fly via a Nested Ensemble Monte Carlo scheme that iteratively queries the energy landscape in regions of failure and updates the training pool to improve the network performance. Using a representative system of gold clusters, we demonstrate that our AL workflow can train a NN with �500 total reference calculations. Using an extensive DFT test set of~1100 configurations, we show that our AL-NN is able to accurately predict both the DFT energies and the forces for clusters of a myriad of different sizes. Our NN predictions are within 30 meV/atom and 40 meV/ Å of the reference DFT calculations. Moreover, our AL-NN model also adequately captures the various size-dependent structural and dynamical properties of gold clusters in excellent agreement with DFT calculations and available experiments. We finally show that our AL-NN model also captures bulk properties reasonably well, even though they were not included in the training data.

Development of Multimodal Machine Learning Potentials: Toward a Physics-Aware Artificial Intelligence

“…Here, the unlabeled data are abundant, but labeling (getting new QM energy) is expensive. Different labeling approaches are known from the literature: Deep Potential Generator (DP-GEN) and AL-NN with a Nested Ensemble Monte Carlo scheme. To develop ANI-1x MLIP, we have generated the AL training data set with an updated on-the-fly via Query by Committee (QBC) algorithm (Figure ).…”

“…Here, the unlabeled data are abundant, but labeling (getting new QM energy) is expensive. Different labeling approaches are known from the literature: Deep Potential Generator (DP-GEN) 44 and AL-NN 45 Transfer Learning…”

dPOLY: Deep Learning of Polymer Phases and Phase Transition

“…We further note that the present work did not aim for developing an ML model with a minimal amount of data; instead, it focused on the proof of concept of an ML-based characterization of polymer phase transformation. Therefore, it is quite possible to build ML models with even lower amounts of data, especially advanced concepts such as active learning to build ML models with sparse data. − Our future works will focus on building an ML-based polymer phase characterization technique with a minimal amount of data and a holistic comparison of the MD–ML approach with a pure MD route across diverse polymeric systems, including chemically realistic models. Although dPOLY is tested for the coil to globule transition, we expect this approach to identify other phase transitions and dynamical crossovers.…”

Machine learning the metastable phase diagram of covalently bonded carbon

“…All calculations were done with an energy cutoff of 600 eV. A dense -point grid defined by , where is the number of atoms in the primitive cell and is the number of -points, is employed 100 , 101 . The phonon modes were computed from the Hessian matrix, obtained from density functional perturbation theory, using the PHONOPY package 102 .…”