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Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…

We present a systematic study that clarifies validity and limitation of current hybrid functionals in density functional theory for structural and electronic properties of various semiconductors and insulators. The three hybrid functionals,…

Double-hybrid density functional theory (DHDFT) offers a pathway to accuracies approaching composite wavefunction approaches like G4 theory. However, the GLPT2 (G{\"o}rling 2nd order perturbation theory) term causes them to partially…

The fourth flight of the Focusing Optics X-ray Solar Imager sounding rocket experiment (FOXSI-4) aimed to achieve the first imaging spectroscopic observations of mid-to-large class ( >= GOES C5 class) solar flares, in contrast to the…

Exchange hole is the principle constituent in density functional theory, which can be used to accurately design exchange energy functional and range separated hybrid functionals coupled with some appropriate correlation. Recently, density…

We provide a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order Moller-Plesset correlation with a semilocal exchange-correlation density functional. These double-hybrid…

We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating…

A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…

A double hybrid approximation using the Coulomb-attenuating method (CAM-DH) is derived within range-separated density-functional perturbation theory, in the spirit of a recent work by Cornaton {\it et al.} [Phys. Rev. A 88, 022516 (2013)].…

We apply the frozen density embedding method, using a full relaxation of embedded densities through a freeze-and-thaw procedure, to study the electronic structure of several benchmark ground-state charge-transfer complexes, in order to…

Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…

LocalSGD and SCAFFOLD are widely used methods in distributed stochastic optimization, with numerous applications in machine learning, large-scale data processing, and federated learning. However, rigorously establishing their theoretical…

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…

We present a rigorous framework that combines single-particle Green's function theory with density functional theory based on a separation of electron-electron interactions into short-range and long-range components. Short-range…

By adopting a divide-and-conquer strategy, subsystem-DFT (sDFT) can dramatically reduce the computational cost of large-scale electronic structure calculations. The key ingredients of sDFT are the nonadditive kinetic energy and…

Since the advent of mesh-free methods as a tool for the numerical analysis of systems of Partial Differential Equations (PDEs), many variants of differential operator approximation have been proposed. In this work, we propose a local…

When applying machine learning to medical image classification, data leakage is a critical issue. Previous methods, such as adding noise to gradients for differential privacy, work well on large datasets like MNIST and CIFAR-100, but fail…

Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for…

Hydrogen bonding is an important non-covalent interaction that plays a major role in molecular self-organization and supramolecular structures. It can be described accurately with ab initio quantum chemical wave function methods, which…

We present DiffXPBD, a novel and efficient analytical formulation for the differentiable position-based simulation of compliant constrained dynamics (XPBD). Our proposed method allows computation of gradients of numerous parameters with…