Related papers: Split representation of adaptively compressed pola…
We propose stochastic splitting algorithms for solving large-scale composite inclusion problems involving monotone and linear operators. They activate at each iteration blocks of randomly selected resolvents of monotone operators and,…
Approximate dynamic programming (ADP) faces challenges in dealing with constraints in control problems. Model predictive control (MPC) is, in comparison, well-known for its accommodation of constraints and stability guarantees, although its…
In this paper we present a novel multiscale splitting approach to solve multiscale Schroedinger equation, which have large different time-scales. The energy potential is based on highly oscillating functions, which are magnitudes faster…
In this paper, we are concerned with a operator splitting scheme for linear fractional and fractional degenerate stochastic conservation laws driven by multiplicative Levy noise. More specifically, using a variant of classical Kruzkov's…
Physically-motivated and mathematically robust atom-centred representations of molecular structures are key to the success of modern atomistic machine learning (ML) methods. They lie at the foundation of a wide range of methods to predict…
The FRiM fractal operator belongs to a family of operators, called ASAP, defined by an ordered selection of nearest neighbors. This generalization provides means to improve upon the good properties of FRiM. We propose a fast algorithm to…
We have developed an effective mathematical model to calculate the coherent population trapping (CPT) resonance in periodically modulated light, when the modulation frequency $f$ varies near the fractional part of hyperfine splitting in the…
We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid…
The Allen-Cahn equation is solved numerically by operator splitting Fourier spectral methods. The basic idea of the operator splitting method is to decompose the original problem into sub-equations and compose the approximate solution of…
Post-training compression of Transformer models commonly relies on truncated singular value decomposition (SVD). However, enforcing a single shared subspace can degrade accuracy even at moderate compression. Sparse dictionary learning…
An extended multi-hadron operator is developed to extract the spectra of irreducible representations in the finite volume. The irreducible representations of the cubic group are projected using a coordinate-space operator. The correlation…
This paper explores a fully discrete approximation for a nonlinear hyperbolic PDE-constrained optimization problem (P) with applications in acoustic full waveform inversion. The optimization problem is primarily complicated by the…
We present a state-of-the-art evaluation of the polarizability corrections--the inelastic nucleon corrections--to the hydrogen ground-state hyperfine splitting using analytic fits to the most recent data. We find a value $\Delta_{\rm pol} =…
A combination of a steady-state preserving operator splitting method and a semi-implicit integration scheme is proposed for efficient time stepping in simulations of unsteady reacting flows, such as turbulent flames, using detailed chemical…
Quantifying materials' dynamical responses to external electromagnetic fields is central to understanding their physical properties. Here we present an implementation of the density functional perturbation theory for the computation of…
Unitary Coupled Cluster (UCC) theory is a promising variational method for electronic structure calculations, especially for strongly correlated systems and quantum computers. However, its practical application is limited by the steep…
The paper studies decentralized optimization over networks, where agents minimize a sum of {\it locally} smooth (strongly) convex losses and plus a nonsmooth convex extended value term. We propose decentralized methods wherein agents {\it…
The transcorrelated (TC) method performs a similarity transformation on the electronic Schr\"odinger equation via Jastrow factorization of the wave function. This has demonstrated significant advancements in computational electronic…
We study electric polarization and nonlinear optical effects in spin systems with broken inversion symmetry. We apply strong coupling expansion to the underlying electronic Hamiltonians, and systematically derive expressions for electric…
The spectral decomposition of a symmetric, second-order tensor is widely adopted in many fields of Computational Mechanics. As an example, in elasto-plasticity under large strain and rotations, given the Cauchy deformation tensor, it is a…