Related papers: A multi-fidelity stochastic collocation method usi…
In this article, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend…
Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper…
Partial differential equation-based numerical solution frameworks for initial and boundary value problems have attained a high degree of complexity. Applied to a wide range of physics with the ultimate goal of enabling engineering…
Supervised deep-embedding methods project inputs of a domain to a representational space in which same-class instances lie near one another and different-class instances lie far apart. We propose a probabilistic method that treats…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
In this paper, we study the numerical stability of reduced order models for convection-dominated stochastic systems in a relatively simple setting: a stochastic Burgers equation with linear multiplicative noise. Our preliminary results…
This paper proposes a novel collocation-type numerical stochastic homogenization method for prototypical stochastic homogenization problems with random coefficient fields of small correlation lengths. The presented method is based on a…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
In this paper, we focus on the construction of a hybrid scheme for the approximation of non-Maxwellian kinetic models with uncertainties. In the context of multiagent systems, the introduction of a kernel at the kinetic level is useful to…
Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…
Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin…
This paper considers the approximation of partial differential equations with a point collocation framework based on high-order local maximum-entropy schemes (HOLMES). In this approach, smooth basis functions are computed through an…
The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection…
We investigate Monte Carlo based algorithms for solving stochastic control problems with probabilistic constraints. Our motivation comes from microgrid management, where the controller tries to optimally dispatch a diesel generator while…
Sequential Monte Carlo (SMC) methods offer a principled approach to Bayesian uncertainty quantification but are traditionally limited by the need for full-batch gradient evaluations. We introduce a scalable variant by incorporating…
Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model,…
This paper considers large-scale linear stochastic systems representing, e.g., spatially discretized stochastic partial differential equations. Since asymptotic stability can often not be ensured in such a stochastic setting (e.g. due to…
In this paper, we study the strong and weak convergence rates for multi-scale one-dimensional stochastic Burgers equation. Based on the techniques of Galerkin approximation, Kolmogorov equation and Poisson equation, we obtain the slow…
In this paper, we study the Crank-Nicolson method for temporal dimension and the piecewise quadratic polynomial collocation method for spatial dimensions of time-dependent nonlocal problems. The new theoretical results of such…
Since their introduction, anchoring methods in extragradient-type saddlepoint problems have inspired a flurry of research due to their ability to provide order-optimal rates of accelerated convergence in very general problem settings. Such…