Related papers: Stein-based preconditioners for weak-constraint 4D…
In this paper, we propose an infinite-dimensional version of the Stein variational gradient descent (iSVGD) method for solving Bayesian inverse problems. The method can generate approximate samples from posteriors efficiently. Based on the…
This paper examines the spatial coverage optimization problem for multiple sensors in a known convex environment, where the coverage service of each sensor is heterogeneous and anisotropic. We introduce the Stein Coverage algorithm, a…
Ensembles of variational data assimilations (EDA) require solving systems of linear equations with iterative methods. The solution process can be accelerated using a limited memory preconditioner constructed with approximations of the…
We introduce $\textit{Stein transport}$, a novel methodology for Bayesian inference designed to efficiently push an ensemble of particles along a predefined curve of tempered probability distributions. The driving vector field is chosen…
This paper addresses variational data assimilation from a learning point of view. Data assimilation aims to reconstruct the time evolution of some state given a series of observations, possibly noisy and irregularly-sampled. Using automatic…
We present a preconditioner for saddle point problems. The proposed preconditioner is extracted from a stationary iterative method which is convergent under a mild condition. Some properties of the preconditioner as well as the eigenvalues…
This paper introduces the Nystr\"om PCG algorithm for solving a symmetric positive-definite linear system. The algorithm applies the randomized Nystr\"om method to form a low-rank approximation of the matrix, which leads to an efficient…
We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semi-definite on an appropriate subspace, Dollar, Gould, Schilders, and Wathen (2006) describe how to apply the…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
We propose a Stein variational gradient descent method to concurrently sparsify, train, and provide uncertainty quantification of a complexly parameterized model such as a neural network. It employs a graph reconciliation and condensation…
This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…
The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random…
Imaging inverse problems are commonly addressed by minimizing measurement consistency and signal prior terms. While huge attention has been paid to developing high-performance priors, even the most advanced signal prior may lose its…
Data assimilation algorithms combine prior and observational information, weighted by their respective uncertainties, to obtain the most likely posterior of a dynamical system. In variational data assimilation the posterior is computed by…
In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…
The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit…
Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…
This paper considers the ill-posed data assimilation problem associated with hyperbolic/parabolic systems describing 2D coupled sound and heat flow. Given hypothetical data at time T > 0, that may not correspond to an actual solution of the…
Most scientific machine learning (SciML) applications of neural networks involve hundreds to thousands of parameters, and hence, uncertainty quantification for such models is plagued by the curse of dimensionality. Using physical…
Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using…