Related papers: Optimized Effective Potentials in Finite Basis Set…
The modified local spin density functional and the related local potential for excited states is tested by employing the ionization potential theorem. The functional is constructed by splitting $k$-space. Since its functional derivative…
This paper investigates continuity properties of value functions and solutions for parametric optimization problems. These problems are important in operations research, control, and economics because optimality equations are their…
In this paper, we address the challenging problem of optimal experimental design (OED) of constrained inverse problems. We consider two OED formulations that allow reducing the experimental costs by minimizing the number of measurements.…
Increasing penetration of renewable energy introduces significant uncertainty into power systems. Traditional simulation-based verification methods may not be applicable due to the unknown-but-bounded feature of the uncertainty sets.…
Covariate balance is a conventional key diagnostic for methods used estimating causal effects from observational studies. Recently, there is an emerging interest in directly incorporating covariate balance in the estimation. We study a…
To mitigate dissipative effects from environmental interactions and efficiently stabilize quantum states, time-optimal control has emerged as an effective strategy for open quantum systems. This paper extends the framework by incorporating…
We use the weighted integral form of spherical Bessel functions, and introduce a new analytical set of complete and biorthogonal potential--density basis functions. The potential and density functions of the new set have finite central…
A unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous…
Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In…
A description of non-collinear magnetism in the framework of spin-density functional theory is presented for the exact exchange energy functional which depends explicitly on two-component spinor orbitals. The equations for the effective…
This paper studies the optimal transmission switching (OTS) problem for power systems, where certain lines are fixed (uncontrollable) and the remaining ones are controllable via on/off switches. The goal is to identify a topology of the…
Embedded density functional theory (e-DFT) is used to describe the electronic structure of strongly interacting molecular subsystems. We present a general implementation of the Exact Embedding (EE) method [J. Chem. Phys. 133, 084103 (2010)]…
The self consistent version of the density functional theory is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems. An exact functional equation for the effective interaction, from…
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…
The quest for a formula that satisfactorily measures the effective degrees of freedom in kernel density estimation (KDE) is a long standing problem with few solutions. Starting from the orthogonal polynomial sequence (OPS) expansion for the…
We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the…
Dynamic operating envelopes (DOEs), as a key enabler to facilitate DER integration, have attracted increasing attention in the past years. However, uncertainties, which may come from load forecast errors or inaccurate network parameters,…
In the last decade, machine learning-based approaches became capable of performing a wide range of complex tasks sometimes better than humans, demanding a fraction of the time. Such an advance is partially due to the exponential growth in…
We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with…
In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set…