Researchers at Google subsidiary DeepMind have open-sourced DM21, a neural network model for mapping electron density to chemical interaction energy, a key component of quantum mechanical simulation. DM21 outperforms traditional models on several benchmarks and is available as an extension to the PySCF simulation framework.
The model was described in an article published in Science. DM21 uses a neural network to approximate the energy density functional component of Density Functional Theory (DFT), which describes the quantum mechanical behavior of molecules. DM21 addresses systemic problems with previous functional approximations, which cannot correctly handle systems with "fractional electron character." The model is based on a multilayer perceptron (MLP) architecture which takes as input a grid of electron densities. When evaluated on three benchmark datasets---Bond-breaking Benchmark (BBB), GMTKN55, and QM9---the model outperformed four of the "best performing" existing implementations. According to the DeepMind team,
As technology increasingly turns to the quantum scale to explore questions about materials, medicines, and catalysts, including those we’ve never seen or even imagined, deep learning shows promise to accurately simulate matter at this quantum mechanical level.
Quantum chemistry is an application of the fundamental rules of quantum physics to predict chemical properties of molecules. DFT provides scientists with a way of simplifying quantum chemistry calculations, but it requires a functional, or mapping from electronic probability densities to energy. Although there is no known exact functional, approximate functionals have been used for many years, in fields from solid-state physics to nuclear spectroscopy.
However, most of the approximations in use encounter "pathological errors" in systems that have characteristics of fractional electrons; in particular, fractional charge (FC) or fractional spin (FS). Although fractional electrons are fictitious, some real systems do have regions that exhibit FC or FS behavior. Because manually designing functionals to handle such cases has proved difficult, the DeepMind team approached the problem using machine learning.
The researchers used a supervised learning approach to train an MLP neural network. The training dataset consisted of 1161 examples; the inputs contained Kohn-Sham (KS) orbital features sampled on a spatial grid, while the output values were "high-accuracy reaction energies." The training objective included both a regression loss and a gradient regularization term; the latter was included so that the model could be used in self-consistent field (SCF) calculations.
The team evaluated DM21 on three benchmarks, including GMTKN55 and QM9, which contain data for chemical tasks "very distinct" from the training data. DM21 set new state-of-the-art performance on these benchmarks, outperforming four other previous methods. According to the researchers, "DM21 is better than the best hybrid functional and approaches the performance of the much more expensive double-hybrid functionals."
The use of machine learning in physics and chemistry is an active research area. In 2019, researchers at Stanford University trained a convolutional neural network (CNN) for use as a DFT functional that achieved good results for "a large set of organic molecules." In 2020, InfoQ reported on Caltech's use of machine learning to solve Navier-Stokes equations, and in 2021 on DeepMind's AlphaFold2 AI for predicting protein structure.
DeepMind's code and pretraind models for DM21 are available on GitHub.