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We introduce an algorithm that can be used to perform stochastic perturbation theory (sPT) to correct any non-linearly parametrized wavefunction that can be optimized using orbital space Variational Monte Carlo (VMC). Although the…
Spectral Photon-Counting Computed Tomography (SPCCT) is a promising technology that has shown a number of advantages over conventional X-ray Computed Tomography (CT) in the form of material separation, artefact removal and enhanced image…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
In this paper, the optimization problem of the supervised distance preserving projection (SDPP) for data dimension reduction (DR) is considered, which is equivalent to a rank constrained least squares semidefinite programming (RCLSSDP). In…
Spatially-coupled (SC) codes are a class of low-density parity-check (LDPC) codes that have excellent performance thanks to the degrees of freedom they offer. An SC code is designed by partitioning a base matrix into components, the number…
In this paper, we propose first-order feasible methods for difference-of-convex (DC) programs with smooth inequality and simple geometric constraints. Our strategy for maintaining feasibility of the iterates is based on a "retraction" idea…
In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…
There is increasing realization in neuroscience that information is represented in the brain, e.g., neocortex, hippocampus, in the form sparse distributed codes (SDCs), a kind of cell assembly. Two essential questions are: a) how are such…
Convergence failure and slow convergence rate are among the biggest challenges with solving the system of non-linear equations numerically. While using strictly small time steps sizes and unconditionally stable fully implicit scheme…
We propose the algorithm that solves the symmetric cone programs (SCPs) by iteratively calling the projection and rescaling methods the algorithms for solving exceptional cases of SCP. Although our algorithm can solve SCPs by itself, we…
The main goal of this paper is to investigate the order reduction phenomenon that appears in the integral deferred correction (InDC) methods based on implicit-explicit (IMEX) Runge-Kutta (R-K) schemes when applied to a class of stiff…
We consider the inverse problem of estimating the initial condition of a partial differential equation, which is only observed through noisy measurements at discrete time intervals. In particular, we focus on the case where Eulerian…
Data parallelism has become the de facto standard for training Deep Neural Network on multiple processing units. In this work we propose DC-S3GD, a decentralized (without Parameter Server) stale-synchronous version of the Delay-Compensated…
A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of…
Purpose: Often, the inverse deformation vector field (DVF) is needed together with the corresponding forward DVF in 4D reconstruction and dose calculation, adaptive radiation therapy, and simultaneous deformable registration. This study…
We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…
In our earlier work [Fareed et al., Comput. Math. Appl. 75 (2018), no. 6, 1942-1960], we developed an incremental approach to compute the proper orthogonal decomposition (POD) of PDE simulation data. Specifically, we developed an…
We propose a new fourth-order compact time-splitting ($S_\text{4c}$) Fourier pseudospectral method for the Dirac equation by splitting the Dirac equation into two parts together with using the double commutator between them to integrate the…
We propose a novel gray-box modeling algorithm for physical systems governed by stochastic differential equations (SDE). The proposed approach, referred to as the Deep Physics Corrector (DPC), blends approximate physics represented in terms…
The interplay between advances in stochastic and deterministic algorithms has recently led to development of interesting new selected configuration interaction (SCI) methods for solving the many body Schr\"{o}dinger equation. The…