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Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In…
We propose a decoherence-free subspaces (DFS) scheme to realize scalable quantum computation with trapped ions. The spin-dependent Coulomb interaction is exploited, and the universal set of unconventional geometric quantum gates is achieved…
The pressure Poisson equation, central to the fractional step method in incompressible flow simulations, incurs high computational costs due to the iterative solution of large-scale linear systems. To address this challenge, we introduce…
Density functional theory (DFT) embedding provides a formally exact framework for interfacing correlated wave-function theory (WFT) methods with lower-level descriptions of electronic structure. Here, we report techniques to improve the…
Extending density functional theory (DFT) to an {\it ab initio} orbital functional theory (OFT) requires new methodology for nonlocal exchange and correlation potentials. This paper describes such modifications to a standard Dirac-Slater…
With the growth of computational resources, the scope of electronic structure simulations has increased greatly. Artificial intelligence and robust data analysis hold the promise to accelerate large-scale simulations and their analysis to…
In this paper, we propose multi-scale deep neural networks (MscaleDNNs) using the idea of radial scaling in frequency domain and activation functions with compact support. The radial scaling converts the problem of approximation of high…
Deploying deep neural networks on edge devices is often limited by the memory traffic and compute cost of dense linear operators. While quaternion neural networks improve parameter efficiency by coupling multiple channels through Hamilton…
With an ever-growing number of parameters defining increasingly complex networks, Deep Learning has led to several breakthroughs surpassing human performance. As a result, data movement for these millions of model parameters causes a…
Density Functional Theory (DFT) is one of the most used ab initio theoretical frameworks in materials science. It derives the ground state properties of a multi-atomic ensemble directly from the computation of its one-particle density \nr…
We provide an overview of high dimensional dynamical systems driven by random matrices, focusing on applications to simple models of learning and generalization in machine learning theory. Using both cavity method arguments and path…
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…
A global hybrid extension of variational two-electron reduced-density matrix (v2RDM)-driven multiconfiguration pair-density functional theory (MCPDFT) is developed. Using a linear decomposition of the electron-electron repulsion term, a…
Recently, machine learning methods have gained significant traction in scientific computing, particularly for solving Partial Differential Equations (PDEs). However, methods based on deep neural networks (DNNs) often lack convergence…
Machine-learning electronic Hamiltonians achieve orders-of-magnitude speedups over density-functional theory, yet current models omit long-range Coulomb interactions that govern physics in polar crystals and heterostructures. We derive…
This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as…
Deep-HP is a scalable extension of the \TinkerHP\ multi-GPUs molecular dynamics (MD) package enabling the use of Pytorch/TensorFlow Deep Neural Networks (DNNs) models. Deep-HP increases DNNs MD capabilities by orders of magnitude offering…
We extend to strongly correlated molecular systems the recently introduced basis-set incompleteness correction based on density-functional theory (DFT) [E. Giner et al., J. Chem. Phys. 149, 194301 (2018)]. This basis-set correction relies…
Deep learning methods for electronic-structure Hamiltonian prediction has offered significant computational efficiency advantages over traditional DFT methods, yet the diversity of atomic types, structural patterns, and the high-dimensional…
We survey approaches to nonrelativistic density functional theory (DFT) for nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using…