Related papers: Stochastic Domain Decomposition Based on Variable-…

This article presents two novel adaptive-sparse polynomial dimensional decomposition (PDD) methods for solving high-dimensional uncertainty quantification problems in computational science and engineering. The methods entail global…

In this letter, we propose a simple yet effective singular value decomposition (SVD) based strategy to reduce the optimization problem dimension in data-enabled predictive control (DeePC). Specifically, in the case of linear time-invariant…

This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we…

We propose a new class of physics-informed neural networks, called physics-informed Variational Autoencoder (PI-VAE), to solve stochastic differential equations (SDEs) or inverse problems involving SDEs. In these problems the governing…

This paper proposes a novel low-rank approximation to the multivariate State-Space Model. The Stochastic Partial Differential Equation (SPDE) approach is applied component-wise to the independent-in-time Mat\'ern Gaussian innovation term in…

This work proposes a method for solving linear stochastic optimal control (SOC) problems using sum of squares and semidefinite programming. Previous work had used polynomial optimization to approximate the value function, requiring a high…

A strategy to construct physics-based local surrogate models for parametric Stokes flows and coupled Stokes-Darcy systems is presented. The methodology relies on the proper generalized decomposition (PGD) method to reduce the dimensionality…

Uncertainty quantification appears today as a crucial point in numerous branches of science and engineering. In the past two decades, a growing interest has been devoted to stochastic finite element method (SFEM) for the propagation of…

The efficient generation of meshes is an important component in the numerical solution of problems in physics and engineering. Of interest are situations where global mesh quality and a tight coupling to the solution of the physical partial…

Inspired by dynamic programming, we propose Stochastic Virtual Gradient Descent (SVGD) algorithm where the Virtual Gradient is defined by computational graph and automatic differentiation. The method is computationally efficient and has…

In this paper, we propose a dynamically low-dimensional approximation method to solve a class of time-dependent multiscale stochastic diffusion equations. A dynamically bi-orthogonal (DyBO) method was developed to explore low-dimensional…

In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…

We extend stochastic basis adaptation and spatial domain decomposition methods to solve time varying stochastic partial differential equations (SPDEs) with a large number of input random parameters. Stochastic basis adaptation allows the…

Two-level domain decomposition (DD) methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level…

This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…

In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…

Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value…

Singular value decomposition (SVD) has a crucial role in model order reduction. It is often utilized in the offline stage to compute basis functions that project the high-dimensional nonlinear problem into a low-dimensionsl model which is,…

This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…

This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC…