相关论文: Parametric Analytical Preconditioning and its Appl…
This paper presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits the domain…
Preconditioning of a linear system obtained from spectral discretization of time-dependent PDEs often results in a full matrix which is expensive to compute and store specially when the problem size increases. A matrix-free implementation…
A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial…
Conformal prediction has emerged as a powerful framework for constructing distribution-free prediction sets with guaranteed coverage assuming only the exchangeability assumption. However, this assumption is often violated in online…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…
Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Current solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and…
This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…
In this paper the authors study a non-linear elliptic-parabolic system, which is motivated by mathematical models for lithium-ion batteries. One state satisfies a parabolic reaction diffusion equation and the other one an elliptic equation.…
Preconditioning is essential in iterative methods for solving linear systems. It is also the implicit objective in updating approximations of Jacobians in optimization methods, e.g.,in quasi-Newton methods. Motivated by the latter, we study…
A preconditioning strategy is proposed for the iterative solve of large numbers of linear systems with parameter-dependent matrix and right-hand side which arise during the computation of solution statistics of stochastic elliptic partial…
A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method,…
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application…
Search engines and recommendation systems attempt to continually improve the quality of the experience they afford to their users. Refining the ranker that produces the lists displayed in response to user requests is an important component…
Conformal Prediction methods have finite-sample distribution-free marginal coverage guarantees. However, they generally do not offer conditional coverage guarantees, which can be important for high-stakes decisions. In this paper, we…
Submodular optimization has received significant attention in both practice and theory, as a wide array of problems in machine learning, auction theory, and combinatorial optimization have submodular structure. In practice, these problems…
When developing robust preconditioners for multiphysics problems, fractional functions of the Laplace operator often arise and need to be inverted. Rational approximation in the uniform norm can be used to convert inverting those fractional…
We consider the computation of averaged coefficients for the homogenization of elliptic partial differential equations. In this problem, like in many multiscale problems, a large number of similar computations parametrized by the…
Preconditioning is a technique from numerical linear algebra that can accelerate algorithms to solve systems of equations. In this paper, we demonstrate how preconditioning can circumvent a stringent assumption for sign consistency in…