Related papers: A kernel compression method for distributed-order …

A novel compressed matrix format is proposed that combines an adaptive hierarchical partitioning of the matrix with low-rank approximation. One typical application is the approximation of discretized functions on rectangular domains; the…

Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…

We introduce an efficient finite-element approach for large-scale real-space pseudopotential density functional theory (DFT) calculations incorporating noncollinear magnetism and spin-orbit coupling. The approach, implemented within the…

We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this…

A high-order accurate adjoint-based optimization framework is presented for unsteady multiphysics problems. The fully discrete adjoint solver relies on the high-order, linearly stable, partitioned solver introduced in [1], where different…

A semi-implicit-explicit (semi-IMEX) Runge-Kutta (RK) method is proposed for the numerical integration of ordinary differential equations (ODEs) of the form $\mathbf{u}' = \mathbf{f}(t,\mathbf{u}) + G(t,\mathbf{u}) \mathbf{u}$, where…

In this paper, we develop fast procedures for solving linear systems arising from discretization of ordinary and partial differential equations with Caputo fractional derivative w.r.t time variable. First, we consider a finite difference…

In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explicit information within the integral terms, but treat boundary…

Solving time-dependent partial differential equations (PDEs) that exhibit sharp gradients or local singularities is computationally demanding, as traditional physics-informed neural networks (PINNs) often suffer from inefficient point…

Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a…

Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…

We propose kernel distributionally robust optimization (Kernel DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel Hilbert spaces (RKHS) to construct a wide range of convex…

We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…

This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…

This paper investigates, a new class of fractional order Runge-Kutta (FORK) methods for numerical approximation to the solution of fractional differential equations (FDEs). By using the Caputo generalizedTaylor formula and the total…

This article aims to develop a direct numerical approach to solve the space-fractional partial differential equations (PDEs) based on a new differential quadrature (DQ) technique. The fractional derivatives are approximated by the weighted…

The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…

This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…

We introduce a refined differentially private (DP) data structure for kernel density estimation (KDE), offering not only improved privacy-utility tradeoff but also better efficiency over prior results. Specifically, we study the…