Related papers: A robust and efficient line search for self-consis…
Gradient-based methods are well-suited for derivative-free optimization (DFO), where finite-difference (FD) estimates are commonly used as gradient surrogates. Traditional stochastic approximation methods, such as Kiefer-Wolfowitz (KW) and…
We study an iterative beam search algorithm for the permutation flowshop (makespan and flowtime minimization). This algorithm combines branching strategies inspired by recent branch-and-bounds and a guidance strategy inspired by the LR…
Line search methods are a prominent class of iterative methods to solve unconstrained minimization problems. These methods produce new iterates utilizing a suitable step size after determining proper directions for minimization. In this…
In this paper, we investigate the energy minimization model of the ensemble Kohn-Sham density functional theory for metallic systems, in which a pseudo-eigenvalue matrix and a general smearing approach are involved. We study the invariance…
We present a new algorithm which is named the Dynamical Functional Particle Method, DFPM. It is based on the idea of formulating a finite dimensional damped dynamical system whose stationary points are the solution to the original…
In this paper, we study a few theoretical issues in the discretized Kohn-Sham (KS) density functional theory (DFT). The equivalence between either a local or global minimizer of the KS total energy minimization problem and the solution to…
We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…
A major challenge in current optimization research for deep learning is to automatically find optimal step sizes for each update step. The optimal step size is closely related to the shape of the loss in the update step direction. However,…
A line search in gradient-based optimization algorithm solves the problem of determining the optimal learning rate for a given gradient or search direction in a single iteration. For most problems, this is determined by evaluating different…
Conformal field theory finds applications across diverse fields, from statistical systems at criticality to quantum gravity through the AdS/CFT correspondence. These theories are subject to strong constraints, enabling a systematic…
The inertial extended Lagrangian/self-consistent field scheme (iEL-SCF) has been adopted for solving charge equilibration in LAMMPS as part of the reactive force field ReaxFF, which due to the charge conservation constraint requires solving…
Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields, ranging from materials science to biochemistry to…
Cascading failures have become a severe threat to interconnected modern power systems. The ultrahigh complexity of the interconnected networks is the main challenge toward the understanding and management of cascading failures. In addition,…
Density functional theory (DFT) has become a standard tool for the study of point defects in materials. However, finding the most stable defective structures remains a very challenging task as it involves the solution of a multimodal…
We formulate a set of equations that facilitate an exact numerical solution of the Kohn-Sham potential for a finite Hubbard chain with nearest neighbour hopping and arbitrary site potentials. The approach relies on a mapping of the…
Many popular first order algorithms for convex optimization, such as forward-backward splitting, Douglas-Rachford splitting, and the alternating direction method of multipliers (ADMM), can be formulated as averaged iteration of a…
Recent works have shown that line search methods greatly increase performance of traditional stochastic gradient descent methods on a variety of datasets and architectures [1], [2]. In this work we succeed in extending line search methods…
Adiabatic connection models (ACMs), which interpolate between the limits of weak and strong interaction, are powerful tools to build accurate exchange-correlation functionals. If the exact weak-interaction expansion from second-order…
We consider descent methods for solving non-finite valued nonsmooth convex-composite optimization problems that employ Gauss-Newton subproblems to determine the iteration update. Specifically, we establish the global convergence properties…
We introduce an efficient stochastic interacting particle-field (SIPF) algorithm with no history dependence for computing aggregation patterns and near singular solutions of parabolic-parabolic Keller-Segel (KS) chemotaxis system in three…