Related papers: Efficient simulations of Hartree--Fock equations b…
This paper introduces the Fej\'er-monotone hybrid steepest descent method (FM-HSDM), a new member to the HSDM family of algorithms, for solving affinely constrained minimization tasks in real Hilbert spaces, where convex smooth and…
Background: The Hartree-Fock mean-field approximation is standard in combination with energy density functionals (EDF) that account for some dynamical correlations. Breaking and restoring the symmetries of the system allow for the inclusion…
We treat the accurate simulation of the calcination reaction in particles, where the particles are large and, thus, the inner-particle processes must be resolved. Because these processes need to be described with coupled partial…
This paper proposes an extra gradient Anderson-accelerated algorithm for solving pseudomonotone variational inequalities, which uses the extra gradient scheme with line search to guarantee the global convergence and Anderson acceleration to…
We consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection…
The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications,…
This study introduces a hybrid fluid simulation approach that integrates generative diffusion models with physics-based simulations, aiming at reducing the computational costs of flow simulations while still honoring all the physical…
This study examines several renowned gradient-based optimization techniques and focuses on their computational efficiency and precision. In the study, the steepest descent, conjugate gradient (Fletcher-Reeves and Polak-Ribiere variants),…
We devise a new accelerated gradient-based estimating sequence technique for solving large-scale optimization problems with composite structure. More specifically, we introduce a new class of estimating functions, which are obtained by…
Separating the Coulomb potential into short-range and long-range components enables the use of different electron repulsion integral algorithms for each component. The short-range part can be efficiently computed using the analytical…
The design of microfluidic devices is a cumbersome and tedious process that can be significantly improved by simulation. Methods based on Computational Fluid Dynamics (CFD) are considered state-of-the-art, but require extensive compute time…
Kinetic simulations are computationally intensive due to six-dimensional phase space discretization. Many kinetic spectral solvers use the asymmetrically weighted Hermite expansion due to its conservation and fluid-kinetic coupling…
We present and compare several many-body methods as applied to two-dimensional quantum dots with circular symmetry. We calculate the approximate ground state energy using a harmonic oscillator basis optimized by Hartree-Fock (HF) theory and…
We classified the decoupled stochastic parallel gradient descent (SPGD) optimization model into two different types: software and hardware decoupling methods. A kind of software decoupling method is then proposed and a kind of hardware…
The linear conjugate gradient method is widely used in physical simulation, particularly for solving large-scale linear systems derived from Newton's method. The nonlinear conjugate gradient method generalizes the conjugate gradient method…
We consider the setting of distributed empirical risk minimization where multiple machines compute the gradients in parallel and a centralized server updates the model parameters. In order to reduce the number of communications required to…
Nonlinear acceleration algorithms improve the performance of iterative methods, such as gradient descent, using the information contained in past iterates. However, their efficiency is still not entirely understood even in the quadratic…
The multiconfigurational time-dependent Hartree-Fock equations are discussed and solved for a one-dimensional model of the Helium atom. Results for the ground state energy and two-particle density as well as the absorption spectrum are…
We present a simple and efficient acceleration technique for an arbitrary method for computing the Euclidean projection of a point onto a convex polytope, defined as the convex hull of a finite number of points, in the case when the number…
We present a higher-order boundary condition for atomistic simulations of dislocations that address the slow convergence of standard supercell methods. The method is based on a multipole expansion of the equilibrium displacement, combining…