Machine-Learning Coupled Cluster Properties through a Density Tensor Representation

Abstract

<div> <div> <div> <p>The introduction of machine-learning (ML) algorithms to quantum mechanics enables rapid evaluation of otherwise intractable expressions at the cost of prior training on appropriate benchmarks. Many computational bottlenecks in the evaluation of accurate electronic structure theory could potentially benefit from the application of such models, from reducing the complexity of the underlying wave function parameter space to circumventing the complications of solving the electronic Schrödinger equation entirely. Applications of ML to electronic structure have thus far been focused on learning molecular properties (mainly the energy) from geometric representations. While this line of study has been quite successful, highly accurate models typically require a “big data” approach with thousands of train- ing data points. Herein, we propose a general, systematically improvable scheme for wave function-based ML of arbitrary molecular properties, inspired by the underlying equations that govern the canonical approach to computing the properties. To this end, we combine the established ML machinery of the t-amplitude tensor representation with a new reduced density matrix representation. The resulting model provides quantitative accuracy in both the electronic energy and dipoles of small molecules using only a few dozen training points per system. </p> </div> </div> </div>

Machine Learning of Coupled Cluster (T)-Energy Corrections via Delta (Δ)-Learning

“…ML-assisted approaches encompass the training of force-fields from ab initio data, prediction of CC amplitudes, and direct energy or property learning using mean-field, correlated, or methods based on density functional theory (DFT). 8 Using DFT densities, it is possible to predict CC energies by leveraging ML: 9 With an iterative approach, Townsend and Vogiatzis et al were able to predict the converged CC amplitudes�hence the CC wave function�by utilizing theoretical properties inherent to Møller−Plesset perturbation theory. 10,11 Another iterative hybrid approach by Maitra et al divides the amplitudes into significant and less significant contributions and reduces computational time without loss of accuracy.…”

Infrared Spectra at Coupled Cluster Accuracy from Neural Network Representations

“…With high-dimensional neural network potentials (NNPs) paving the way, 14−16 a multitude of different techniques have been developed to create highly accurate models of interactions; 17−24 see in particular ref 25 for a detailed review with a focus on small molecules and reactions. In recent years, ML approaches have progressed toward the description of properties, such as polarizabilities 26 or dipole moments 27,28 which modulate the IR spectral intensities. This was first shown for electric dipole moments in ref 27 based on environment-dependent charges represented by neural networks.…”

Machine Learning Diffusion Monte Carlo Energies

“…14 Several studies have utilized machine learning to predict quantities computed using MP2 or CCSD(T). 15−20 In ref 16, a novel representation, called the density tensor representation, was introduced and was used to predict accurate energies and dipoles of small molecules at the MP2 level. In ref 19, the density Δ-DFT approach was introduced and utilized for small molecules.…”