相关论文: Goal-Oriented Adaptive THB-Spline Schemes for PDE-…
Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing…
In the absence of labeled target data, unsupervised domain adaptation approaches seek to align the marginal distributions of the source and target domains in order to train a classifier for the target. Unsupervised domain alignment…
We present an adaptive scheme for isogeometric phase-field modeling, to perform suitably graded hierarchical refinement and coarsening on both single- and multi-patch geometries by considering truncated hierarchical spline constructions…
This work introduces and analyzes B-spline approximation spaces defined on general geometric domains obtained through a mapping from a parameter domain. These spaces are constructed as sparse-grid tensor products of univariate spaces in the…
We propose an efficient estimation technique for the automatic selection of locally-adaptive Total Variation regularisation parameters based on an hybrid strategy which combines a local maximum-likelihood approach estimating space-variant…
Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…
A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous…
Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive…
This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain…
We present numerical experiments for geophysics electromagnetic (EM) modeling based upon high-order edge elements and supervised $h+p$ refinement approaches on massively parallel computers. Our high-order $h+p$ refinement strategy is based…
Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…
Preference tuning aligns pretrained language models to human judgments of quality, helpfulness, or safety by optimizing over explicit preference signals rather than likelihood alone. Prior work has shown that preference-tuning degrades…
The numerical approximation of solutions of parametric or stochastic hyperbolic PDEs is still a serious challenge. Because of shock singularities, most methods from the elliptic and parabolic regime, such as reduced basis methods, POD or…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
In the present paper non-convex multi-objective parameter optimization problems are considered which are governed by elliptic parametrized partial differential equations (PDEs). To solve these problems numerically the Pascoletti-Serafini…
We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a…
In this paper, we investigate the channel estimation problem for extremely large-scale multiple-input multiple-output (XL-MIMO) systems with a hybrid analog-digital architecture, implemented within a decentralized baseband processing (DBP)…
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline…
As one of the fundamental tasks in computer vision, semantic segmentation plays an important role in real world applications. Although numerous deep learning models have made notable progress on several mainstream datasets with the rapid…
We present a method for approximating the solution of a parameterized, nonlinear dynamical system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are…