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We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we…
Consider the problem of determining the optimal applied electric field to drive a molecule from an initial state to a desired target state. For even moderately sized molecules, solving this problem directly using the exact equations of…
Federated Learning is a popular distributed learning paradigm in machine learning. Meanwhile, composition optimization is an effective hierarchical learning model, which appears in many machine learning applications such as meta learning…
The optimal power flow (OPF) problem is fundamental in power system operations and planning. Large-scale renewable penetration in distribution networks calls for real-time feedback control, and hence the need for fast and distributed…
The alternating-current optimal power flow (ACOPF) is one of the best known non-convex non-linear optimisation problems. We present a novel re-formulation of ACOPF, which is based on lifting the rectangular power-voltage rank-constrained…
In this paper, we consider the problem of optimally coordinating the response of a group of distributed energy resources (DERs) in distribution systems by solving the so-called optimal power flow (OPF) problem. The OPF problem is concerned…
Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real…
Optimal damping aims at determining a vector of damping coefficients $\nu$ that maximizes the decay rate of a mechanical system's response. This problem can be formulated as the minimization of the trace of the solution of a Lyapunov…
A novel derivative-free algorithm, optimization by moving ridge functions (OMoRF), for unconstrained and bound-constrained optimization is presented. This algorithm couples trust region methodologies with output-based dimension reduction to…
This study presents an evaluation of derivative-free optimization algorithms for the direct minimization of Hartree-Fock-Roothaan energy functionals involving nonlinear orbital parameters and quantum numbers with noninteger order. The…
Repeated computations on the same molecular system, but with different geometries, are often performed in quantum chemistry, for instance, in ab-initio molecular dynamics simulations or geometry optimizations. While many efficient…
This article examines the time-dependent Hartree-Fock (TDHF) approximation of single-particle dynamics in systems of interacting fermions. We find the TDHF approximation to be accurate when there are sufficiently many particles and the…
Designing robust algorithms for the optimal power flow (OPF) problem is critical for the control of large-scale power systems under uncertainty. The chance-constrained OPF (CCOPF) problem provides a natural formulation of the trade-off…
The multiconfiguration time-dependent Hartree-Fock (MCTDHF) method is formulated for treating the coupled electronic and nuclear dynamics of diatomic molecules without the Born- Oppenheimer approximation. The method treats the full…
This paper proposes a convex optimization based distributed algorithm to solve multi-period optimal gas-power flow (OGPF) in coupled energy distribution systems. At the gas distribution system side, the non-convex Weymouth gas flow…
In periodic systems, the Hartree-Fock (HF) exchange energy exhibits the slowest convergence of all HF energy components as the system size approaches the thermodynamic limit. We demonstrate that the recently proposed staggered mesh method…
The Optimal power flow (OPF) problem contains many constraints. However, equality constraints along with a limited set of active inequality constraints encompass sufficient information to determine the feasible space of the problem. In this…
Managing uncertainty and variability in power injections has become a major concern for power system operators due to the increasing levels of fluctuating renewable energy connected to the grid. This work addresses this uncertainty via a…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
We propose a hierarchical distributed algorithm to solve optimal power flow (OPF) problems that aim at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm features…