Related papers: The Truncated Conjugate Gradient (TCG), a Non-iter…
I development a Conjugate Gradient Method for solving a partial differential system with multiply controls. Some numerical results are depicted. Also, I present an explication of why the control over a partial differential equations system…
Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…
In Coupled-Cluster (CC) theory, unphysical complex energies may arise in the presence of strong magnetic fields, near conical intersections, or in systems exhibiting complex Abelian point group symmetries. This issue originates from the…
This note proposes an efficient preconditioner for solving linear and semi-linear parabolic equations. With the Crank-Nicholson time stepping method, the algebraic system of equations at each time step is solved with the conjugate gradient…
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…
The theoretical prediction of the rates of nonradiative processes in molecules is fundamental to assess their emissive properties. In this context, global harmonic models have been widely used to simulate vibronic spectra as well as…
Contingency analysis (CA) plays a critical role to guarantee operation security in the modern power systems. With the high penetration of renewable energy, a real-time and comprehensive N-1 CA is needed as a power system analysis tool to…
An estimation of the sky signal from streams of Time Ordered Data (TOD) acquired by Cosmic Microwave Background (\cmb) experiments is one of the most important steps in the context of \cmb data analysis referred to as the map-making…
We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behaviour of a coupled cluster wavefunction representation…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
This paper introduces Tempered Fractional Gradient Descent (TFGD), a novel optimization framework that synergizes fractional calculus with exponential tempering to enhance gradient-based learning. Traditional gradient descent methods often…
Linear solvers are key components in any software platform for scientific and engineering computing. The solution of large and sparse linear systems lies at the core of physics-driven numerical simulations relying on partial differential…
A structured preconditioned conjugate gradient (PCG) solver is developed for the Newton steps in second-order methods for a class of constrained network optimal control problems. Of specific interest are problems with discrete-time dynamics…
We describe a technique for constraining macroscopic fluctuations in thermodynamic variables well-suited for Monte Carlo (MC) simulations of multiphase equilibria. In particular for multicomponent systems this amounts to a statistical…
We deduce a procedure to apply balanced truncation to parameter-dependent differential-algebraic systems. For that we solve multiple projected Lyapunov equations for different parameter values to compute the Gramians that are required for…
In the long-time pursuit of the solution to calculate the partition function (or free energy) of condensed matter, Monte-Carlo-based nested sampling should be the state-of-the-art method, and very recently, we established a direct integral…
Decentralized learning over distributed datasets can have significantly different data distributions across the agents. The current state-of-the-art decentralized algorithms mostly assume the data distributions to be Independent and…
Coarse-grained (CG) molecular dynamics (MD) simulations can simulate large molecular complexes over extended timescales by reducing degrees of freedom. A critical step in CG modeling is the selection of the CG mapping algorithm, which…
Analytical forces have been derived in the Lagrangian framework for several random phase approximation (RPA) correlated total energy methods based on the range separated hybrid (RSH) approach, which combines a short-range density functional…
We introduce a new method to simulate the physics of rare events. The method, an extension of the Temperature Accelerated Molecular Dynamics, comes in use when the collective variables introduced to characterize the rare events are either…