Related papers: A non-adapted sparse approximation of PDEs with st…
We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs. The algorithm is employed to approximate stochastic…
In this paper, we discuss the numerical approximation of random periodic solutions (r.p.s.) of stochastic differential equations (SDEs) with multiplicative noise. We prove the existence of the random periodic solution as the limit of the…
This work introduces the StoMADS-PB algorithm for constrained stochastic blackbox optimization, which is an extension of the mesh adaptive direct-search (MADS) method originally developed for deterministic blackbox optimization under…
In this work we study convergence properties of sparse polynomial approximations for a class of affine parametric saddle point problems. Such problems can be found in many computational science and engineering fields, including the Stokes…
In this work, we consider the Biot problem with uncertain poroelastic coefficients. The uncertainty is modelled using a finite set of parameters with prescribed probability distribution. We present the variational formulation of the…
We propose a novel adaptive empirical Bayesian method for sparse deep learning, where the sparsity is ensured via a class of self-adaptive spike-and-slab priors. The proposed method works by alternatively sampling from an adaptive…
We propose a sampling-based trajectory optimization methodology for constrained problems. We extend recent works on stochastic search to deal with box control constraints,as well as nonlinear state constraints for discrete dynamical…
This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white noise driven stochastic partial differential equations…
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…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
We present a novel solution method for It\^o stochastic differential equations (SDEs). We subdivide the time interval into sub-intervals, then we use the quadratic polynomials for the approximation between two successive intervals. The main…
Stochastic optimisation problems minimise expectations of random cost functions. We use 'optimise then discretise' method to solve stochastic optimisation. In our approach, accurate quadrature methods are required to calculate the…
This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue…
This work introduces StoMADS, a stochastic variant of the mesh adaptive direct-search (MADS) algorithm originally developed for deterministic blackbox optimization. StoMADS considers the unconstrained optimization of an objective function f…
This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems. The main tools are the graphical models and approximate message-passing algorithm together with the cavity…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
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 present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…