Related papers: A bi-fidelity stochastic collocation method for tr…
In this paper, we introduce a bi-fidelity algorithm for velocity discretization of Boltzmann-type kinetic equations under multiple scales. The proposed method employs a simpler and computationally cheaper low-fidelity model to capture a…
In this paper, we study the multiscale Boltzmann equation with multi-dimensional random parameters by a bi-fidelity stochastic collocation (SC) method developed in [A. Narayan, C. Gittelson and D. Xiu, SIAM J. Sci. Comput., 36 (2014); X.…
Uncertainty in data is certainly one of the main problems in epidemiology, as shown by the recent COVID-19 pandemic. The need for efficient methods capable of quantifying uncertainty in the mathematical model is essential in order to…
We introduce a dynamical low-rank method to reduce the computational complexity for solving the multi-scale multi-dimensional linear transport equation. The method is based on a macro-micro decomposition of the equation. The proposed…
For linear transport and radiative heat transfer equations with random inputs, we develop new generalized polynomial chaos based Asymptotic-Preserving stochastic Galerkin schemes that allow efficient computation for the problems that…
Stochastic optimization of engineering systems is often infeasible due to repeated evaluations of a computationally expensive, high-fidelity simulation. Bi-fidelity methods mitigate this challenge by leveraging a cheaper, approximate model…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…
In traffic flow modeling, incorporating uncertainty is crucial for accurately capturing the complexities of real-world scenarios. In this work we focus on kinetic models of traffic flow, where a key step is to design effective numerical…
In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist.…
High-quality spatiotemporal traffic data is crucial for intelligent transportation systems (ITS) and their data-driven applications. Inevitably, the issue of missing data caused by various disturbances threatens the reliability of data…
In this paper, we deal with the convergence of an iterative scheme for the 2-D stochastic Navier-Stokes Equations on the torus suggested by the Lie-Trotter product formulas for stochastic differential equations of parabolic type. The…
Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori…
Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…
Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…
In this paper a drift-randomized Milstein method is introduced for the numerical solution of non-autonomous stochastic differential equations with non-differentiable drift coefficient functions. Compared to standard Milstein-type methods we…
We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…
This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a…