Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids

Jørgensen, Peter Bjørn; Bhowmik, Arghya

doi:10.1038/s41524-022-00863-y

Cited by 27 publications

(26 citation statements)

References 66 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, as shown in the lower panel of the Figure, absolute density errors integrated on a real-space grid are distributed around a mean absolute error of 0.45%, which is about 25% larger than those observed for liquid water. When compared with the results of ref for the very same QM9 test molecules, we find that our errors are about 1.5 times larger; this is still remarkable when considering that we used only 6% of the training set and that we predict the all-electron density, whereas ref uses almost the entire QM9 data set and uses the pseudovalence density as the target. In Figure we also report learning curves and error histogram for the derived total energy predictions, showing a mean absolute error that is brought down to 1.57 kcal/mol, with 65% of our predictions falling within chemical accuracy.…”

Section: Resultsmentioning

confidence: 74%

“…In testing the accuracy of our predictions we rely on the same partitioning of the data set reported in ref ; i.e., using the same random selection of 10 000 structures as a test set, while using the remaining configurations for training the model. In order to directly compare our results with what is reported in ref , we also make use of the same local environment definition by selecting a radial cutoff around the atoms of r cut = 4 Å. For all learning exercises, we consider active set sizes that span M = {2500, 5000, 10000}.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Electronic-Structure Properties from Atom-Centered Predictions of the Electron Density

Grisafi

Lewis

Rossi

et al. 2022

J. Chem. Theory Comput.

View full text Add to dashboard Cite

The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to represent the scalar field using a multicentered atomic basis analogous to that routinely used in density fitting approximations. However, the nonorthogonality of the basis poses challenges for the learning exercise, as it requires accounting for all the atomic density components at once. We devise a gradient-based approach to directly minimize the loss function of the regression problem in an optimized and highly sparse feature space. In so doing, we overcome the limitations associated with adopting an atom-centered model to learn the electron density over arbitrarily complex data sets, obtaining very accurate predictions using a comparatively small training set. The enhanced framework is tested on 32-molecule periodic cells of liquid water, presenting enough complexity to require an optimal balance between accuracy and computational efficiency. We show that starting from the predicted density a single Kohn–Sham diagonalization step can be performed to access total energy components that carry an error of just 0.1 meV/atom with respect to the reference density functional calculations. Finally, we test our method on the highly heterogeneous QM9 benchmark data set, showing that a small fraction of the training data is enough to derive ground-state total energies within chemical accuracy.

show abstract

Section: Resultsmentioning

confidence: 74%

Section: Resultsmentioning

confidence: 99%

Electronic-Structure Properties from Atom-Centered Predictions of the Electron Density

Grisafi

Lewis

Rossi

et al. 2022

J. Chem. Theory Comput.

View full text Add to dashboard Cite

show abstract

“…ερ for each molecule in the test sets is computed using a 3D cubic grid of voxel spacing (0.2, 0.2, 0.2) Bohr for the BFDb-SSI test set and voxel spacing (1.0, 1.0, 1.0) Bohr for the QM9 test set, both with cutoffs at ρ( r) = 10 −5 a −3 0 . We note that two baseline methods used slightly different normalization conventions when computing the dataset-averaged L 1 density errors ερ: 1) computing ερ for each molecule and normalizing over the number of molecules in the test set (62) or 2) normalizing over the total number of electrons in the test set (61). We found that the average ερ computed using normalization 2 is higher than normalization 1 by around 5% for our results.…”

Section: Each Neuron In H Tmentioning

confidence: 74%

“…(Materials and M ethods); specifically, OrbNet-Equi achieves an average ε ρ of 0.191 ± 0.003% on BfDB-SSI using 2,000 training samples compared with 0.29% of Symmetry-Adapted Gaussian Process Regression (61) and an average ε ρ of 0.206 ± 0.001% on QM9 using 123,835 training samples as compared with 0.28 to 0.36% of DeepDFT (62). Fig.…”

Section: Resultsmentioning

confidence: 95%

“…Benchmarking details and summary statistics. For the mean L 1 electronic density error over the test sets reported in Accurate Modeling for Electron Densities, we used 291 dimers as the test set for the BFDb-SSI dataset and 10,000 molecules as the test set for the QM9 dataset following the literature (61,62). ερ for each molecule in the test sets is computed using a 3D cubic grid of voxel spacing (0.2, 0.2, 0.2) Bohr for the BFDb-SSI test set and voxel spacing (1.0, 1.0, 1.0) Bohr for the QM9 test set, both with cutoffs at ρ( r) = 10 −5 a −3 0 .…”

Section: Each Neuron In H Tmentioning

confidence: 99%

See 1 more Smart Citation

Informing geometric deep learning with electronic interactions to accelerate quantum chemistry

Qiao

Christensen²,

Welborn³

et al. 2022

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

Predicting electronic energies, densities, and related chemical properties can facilitate the discovery of novel catalysts, medicines, and battery materials. However, existing machine learning techniques are challenged by the scarcity of training data when exploring unknown chemical spaces. We overcome this barrier by systematically incorporating knowledge of molecular electronic structure into deep learning. By developing a physics-inspired equivariant neural network, we introduce a method to learn molecular representations based on the electronic interactions among atomic orbitals. Our method, OrbNet-Equi, leverages efficient tight-binding simulations and learned mappings to recover high-fidelity physical quantities. OrbNet-Equi accurately models a wide spectrum of target properties while being several orders of magnitude faster than density functional theory. Despite only using training samples collected from readily available small-molecule libraries, OrbNet-Equi outperforms traditional semiempirical and machine learning–based methods on comprehensive downstream benchmarks that encompass diverse main-group chemical processes. Our method also describes interactions in challenging charge-transfer complexes and open-shell systems. We anticipate that the strategy presented here will help to expand opportunities for studies in chemistry and materials science, where the acquisition of experimental or reference training data is costly.

show abstract

Recent Advances in Machine Learning‐Assisted Multiscale Design of Energy Materials

Mortazavi

2024

Advanced Energy Materials

View full text Add to dashboard Cite

This review highlights recent advances in machine learning (ML)‐assisted design of energy materials. Initially, ML algorithms were successfully applied to screen materials databases by establishing complex relationships between atomic structures and their resulting properties, thus accelerating the identification of candidates with desirable properties. Recently, the development of highly accurate ML interatomic potentials and generative models has not only improved the robust prediction of physical properties, but also significantly accelerated the discovery of materials. In the past couple of years, ML methods have enabled high‐precision first‐principles predictions of electronic and optical properties for large systems, providing unprecedented opportunities in materials science. Furthermore, ML‐assisted microstructure reconstruction and physics‐informed solutions for partial differential equations have facilitated the understanding of microstructure–property relationships. Most recently, the seamless integration of various ML platforms has led to the emergence of autonomous laboratories that combine quantum mechanical calculations, large language models, and experimental validations, fundamentally transforming the traditional approach to novel materials synthesis. While highlighting the aforementioned recent advances, existing challenges are also discussed. Ultimately, ML is expected to fully integrate atomic‐scale simulations, reverse engineering, process optimization, and device fabrication, empowering autonomous and generative energy system design. This will drive transformative innovations in energy conversion, storage, and harvesting technologies.

show abstract

Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids

Abstract: Electron density $$\rho (\overrightarrow{{{{\bf{r}}}}})$$ ρ ( r → ) is the fundamental variable in the calculation of ground state energy with density… Show more

Cited by 27 publications

References 66 publications

Electronic-Structure Properties from Atom-Centered Predictions of the Electron Density

Electronic-Structure Properties from Atom-Centered Predictions of the Electron Density

Informing geometric deep learning with electronic interactions to accelerate quantum chemistry

Recent Advances in Machine Learning‐Assisted Multiscale Design of Energy Materials

Contact Info

Product

Resources

About