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The calculation of electron density distribution using density functional theory (DFT) in materials and molecules is central to the study of their quantum and macro-scale properties, yet accurate and efficient calculation remains a…

Hamiltonian matrix prediction is pivotal in computational chemistry, serving as the foundation for determining a wide range of molecular properties. While SE(3) equivariant graph neural networks have achieved remarkable success in this…

End-to-end prediction of high-order crystal tensor properties from atomic structures remains challenging: while spherical-harmonic equivariant models are expressive, their Clebsch-Gordan tensor products incur substantial compute and memory…

Predicting quantum operator matrices such as Hamiltonian, overlap, and density matrices in the density functional theory (DFT) framework is crucial for material science. Current methods often focus on individual operators and struggle with…

Deep learning electronic structures from ab initio calculations holds great potential to revolutionize computational materials studies. While existing methods proved success in deep-learning density functional theory (DFT) Hamiltonian…

Deep learning for predicting the electronic-structure Hamiltonian of quantum systems necessitates satisfying the covariance laws, among which achieving SO(3)-equivariance without sacrificing the non-linear expressive capability of networks…

Hamiltonian neural networks (HNNs) represent a promising class of physics-informed deep learning methods that utilize Hamiltonian theory as foundational knowledge within neural networks. However, their direct application to engineering…

By conceiving physical systems as 3D many-body point clouds, geometric graph neural networks (GNNs), such as SE(3)/E(3) equivalent GNNs, have showcased promising performance. In particular, their effective message-passing mechanics make…

Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus…

We consider the task of predicting Hamiltonian matrices to accelerate electronic structure calculations, which plays an important role in physics, chemistry, and materials science. Motivated by the inherent relationship between the…

Computational materials discovery is limited by the high cost of first-principles calculations. Machine learning (ML) potentials that predict energies from crystal structures are promising, but existing methods face computational…

Density-functional theory with extended Hubbard functionals (DFT+$U$+$V$) provides a robust framework to accurately describe complex materials containing transition-metal or rare-earth elements. It does so by mitigating self-interaction…

The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and…

The discovery and optimization of high-energy materials (HEMs) are constrained by the prohibitive computational expense and prolonged development cycles inherent in conventional approaches. In this work, we develop a general neural network…

Atomistic machine learning focuses on the creation of models which obey fundamental symmetries of atomistic configurations, such as permutation, translation, and rotation invariances. In many of these schemes, translation and rotation…

We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…

Deep neural networks (DNNs) have enabled impressive breakthroughs in various artificial intelligence (AI) applications recently due to its capability of learning high-level features from big data. However, the current demand of DNNs for…

Moir\'e-twisted materials have garnered significant research interest due to their distinctive properties and intriguing physics. However, conducting first-principles studies on such materials faces challenges, notably the formidable…

High-entropy alloys (HEAs) exhibit exceptional properties arising from a combination of thermodynamic, kinetic and structural factors and have found applications in numerous fields such as aerospace, energy, chemical industries, hydrogen…

While density functional theory (DFT) serves as a prevalent computational approach in electronic structure calculations, its computational demands and scalability limitations persist. Recently, leveraging neural networks to parameterize the…