Machine Learning Diffusion Monte Carlo Forces

Abstract

Diffusion Monte Carlo (DMC) is one of the most accurate techniques available for calculating the electronic properties of molecules and materials, yet it often remains a challenge to economically compute forces using this technique. As a result, ab initio molecular dynamics simulations and geometry optimizations that employ Diffusion Monte Carlo forces are often out of reach. One potential approach for accelerating the computation of "DMC forces" is to machine learn these forces from DMC energy calculations. In this work, we employ Behler−Parrinello Neural Networks to learn DMC forces from DMC energy calculations for geometry optimization and molecular dynamics simulations of small molecules. We illustrate the unique challenges that stem from learning forces without explicit force data and from noisy energy data by making rigorous comparisons of potential energy surface, dynamics, and optimization predictions among ab initio density functional theory (DFT) simulations and machine-learning models trained on DFT energies with forces, DFT energies without forces, and DMC energies without forces. We show for three small molecules�C 2 , H 2 O, and CH 3 Cl�that machine-learned DMC dynamics can reproduce average bond lengths and angles within a few percent of known experimental results at one hundredth of the typical cost. Our work describes a much-needed means of performing dynamics simulations on high-accuracy, DMC PESs and for generating DMC-quality molecular geometries given current algorithmic constraints.

Data-Efficient Machine Learning Potentials from Transfer Learning of Periodic Correlated Electronic Structure Methods: Liquid Water at AFQMC, CCSD, and CCSD(T) Accuracy

“…Machine-learned potentials (MLPs) have emerged as an extremely promising approach to accurately model ab initio potential energy surfaces of condensed-phase systems while being orders of magnitude more computationally efficient to evaluate. For liquid water, MLPs have been successfully developed at various levels of electronic structure ranging from different levels of DFT − to, more recently, using the random phase approximation (RPA) and MP2. , The modeling of liquid water and other molecular systems with more accurate electronic structure methods, such as coupled-cluster theory or quantum Monte Carlo, has been limited, so far, to training on finite clusters of molecules. − When training on small clusters, higher-order many-body interactions must be included by other means such as by using the TTM4-F potential, as is done for the MB-Pol water model. − Other cluster-based models for water have gone on to explicitly include 4-body terms − and also train on larger water clusters . MLPs fit to periodic electronic structure offer the opportunity to readily capture many-body electronic structure effects, since these are naturally included in the electronic structure calculation.…”

Training models using forces computed by stochastic electronic structure methods

“…For generating ML data, the efficiency, namely how much computer resources are needed to reach a given error on the forces is important. Huang and Rubenstein [13] have discussed recent methods to calculate forces using QMC. More research is needed on the relative efficiencies, the biases, and the appropriate domains of the QMC methods for the calculation of accurate forces.…”

“…Also forces give local information and integrate well with the ML models which are also local. Use of only the QMC energies to determine the ML model, as was done in [13], requires many more QMC calculations and results in a much less accurate PES. The likelihood function for optimizing the model including both energies and forces is…”

“…We examine in this paper whether stochastic methods, such as variational and diffusion quantum Monte Carlo (QMC) can be used to provide the training data so that the resulting model will be more accurate. Such an approach has been considered previously, for example in work by Alfe et al [9], Sorella et al [10,11], Niu et al [12], Huang and Rubenstein [13], Nakano et al [14] and Cheng et al [15]. But several aspects of this approach, such as the effects of the noise on the model, have only been touched on [13].…”

“…Such an approach has been considered previously, for example in work by Alfe et al [9], Sorella et al [10,11], Niu et al [12], Huang and Rubenstein [13], Nakano et al [14] and Cheng et al [15]. But several aspects of this approach, such as the effects of the noise on the model, have only been touched on [13].…”