相关论文: The Quantum and Stochastic Toolbox: xSPDE4.2
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…
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…
A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, and…
Differential Equations are among the most important Mathematical tools used in creating models in the science, engineering, economics, mathematics, physics, aeronautics, astronomy, dynamics, biology, chemistry, medicine, environmental…
The Statistical Toolkit is an open source system specialized in the statistical comparison of distributions. It addresses requirements common to different experimental domains, such as simulation validation (e.g. comparison of experimental…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
QPot is an R package for analyzing two-dimensional systems of stochastic differential equations. It provides users with a wide range of tools to simulate, analyze, and visualize the dynamics of these systems. One of QPot's key features is…
This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is…
Backward Stochastic Differential Equations (BSDEs) have been widely employed in various areas of social and natural sciences, such as the pricing and hedging of financial derivatives, stochastic optimal control problems, optimal stopping…
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…
Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the…
A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form $L^{\beta}u = \mathcal{W}$, where $\mathcal{W}$ is…
Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of…
Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parameters, constitutive relations, initial/boundary conditions,…
We introduce and study a new class of partial differential equations (PDEs) with hybrid fuzzy-stochastic parameters, coined fuzzy-stochastic PDEs. Compared to purely stochastic PDEs or purely fuzzy PDEs, fuzzy-stochastic PDEs offer powerful…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
Quantum Phase Estimation (QPE) is a cornerstone algorithm in quantum computing, with applications ranging from integer factorization to quantum chemistry simulations. However, the resource demands of standard QPE, which require a large…
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…
The intrusive (sample-free) spectral stochastic finite element method (SSFEM) is a powerful numerical tool for solving stochastic partial differential equations (PDEs). However, it is not widely adopted in academic and industrial…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…