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The recently developed Deep Potential [Phys. Rev. Lett. 120, 143001, 2018] is a powerful method to represent general inter-atomic potentials using deep neural networks. The success of Deep Potential rests on the proper treatment of locality…

We introduce an efficient finite-element approach for large-scale real-space pseudopotential density functional theory (DFT) calculations incorporating noncollinear magnetism and spin-orbit coupling. The approach, implemented within the…

Aspects of Density Functional Resonance Theory (DFRT) [Phys. Rev. Lett. \textbf{107}, 163002 (2011)], a recently developed complex-scaled version of ground-state Density Functional Theory (DFT), are studied in detail. The asymptotic…

HF-DFT, the practice of evaluating approximate density functionals on Hartree-Fock densities, has long been used in testing density functional approximations. Density-corrected DFT (DC-DFT) is a general theoretical framework for identifying…

The accurate modeling of spin-orbit coupling (SOC) effects in diverse complex systems remains a significant challenge due to the high computational demands of density functional theory (DFT) and the limited transferability of existing…

This chapter presents the development of a density functional theory (DFT)-based method for accurate, reliable treatment of various resonances in atoms. Many of these are known to be notorious for their strong correlation, proximity to more…

To accurately compute data-based prediction of Hamiltonian systems, especially the long-term evolution of such systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a case that is…

Density functional theory (DFT) is the de facto approach for predicting self-consistent-field electronic structures of ground-state configurations of complex atoms, molecules, and solids and providing their property data for materials…

Density functional theory (DFT) became a universal approach to compute ground-state and excited configurations of many-electron systems held together by an external one-body potential in condensed-matter, atomic, and molecular physics. At…

Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to…

Understanding how deep learning architectures work is a central scientific problem. Recently, a correspondence between neural networks (NNs) and Euclidean quantum field theories (QFTs) has been proposed. This work investigates this…

Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availability of high-performance computing infrastructure, many…

Machine learning has made important headway in helping to improve the treatment of quantum many-body systems. A domain of particular relevance are correlated inhomogeneous systems. What has been missing so far is a general, scalable…

Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach. The search…

Density functional theory (DFT) provides a theoretical framework for efficient and fairly accurate calculations of the electronic structure of molecules and crystals. The main features of density functional theory are described and DFT…

We derive an exact representation of the exchange-correlation energy within density functional theory (DFT) which spawns a class of approximations leading to correct long-range asymptotic behavior. In what amounts to be the simplest…

Delocalization errors, such as charge-transfer and some self-interaction errors, plague computationally-efficient and otherwise-accurate density functional approximations (DFAs). Evaluating a semi-local DFA non-self-consistently on the…

We introduce the unification of dynamical mean field theory (DMFT) and linear-scaling density functional theory (DFT), as recently implemented in ONETEP, a linear-scaling DFT package, and TOSCAM, a DMFT toolbox. This code can account for…

We present a new method to solve the nuclear density functional theory (DFT) equations using a two-center harmonic oscillator for Skyrme-like functionals, incorporating pairing and Coulomb interactions. The goal is to efficiently determine…

The development of systematic effective field theories (EFTs) for nuclear forces and advances in solving the nuclear many-body problem have greatly improved our understanding of dense nuclear matter and the structure of finite nuclei. For…