相关论文: Goal-Oriented Adaptive THB-Spline Schemes for PDE-…

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical…

We formulate and analyze a goal-oriented adaptive finite element method for a symmetric linear elliptic partial differential equation (PDE) that can simultaneously deal with multiple linear goal functionals. In each step of the algorithm,…

This paper derives a new class of adaptive regularization parameter choice strategies that can be effectively and efficiently applied when regularizing large-scale linear inverse problems by combining standard Tikhonov regularization and…

We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…

Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…

Real-time path tracing increasingly operates under extremely low sampling budgets, often below one sample per pixel, as rendering complexity, resolution, and frame-rate requirements continue to rise. While super-resolution is widely used in…

This article proposes a new approach based on finite-horizon parameterizing manifolds (PMs) for the design of low-dimensional suboptimal controllers to optimal control problems of nonlinear partial differential equations (PDEs) of parabolic…

Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…

A method is created to automatically increase the threshold projection parameter in three-field density-based topology optimization to achieve a near binary design. The parameter increase each iteration is based on an exponential growth…

The novel Locally Refined B-spline (LR B-spline) surface format is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline…

We propose two optimization-based heuristics for structure selection and identification of PieceWise Affine (PWA) models with exogenous inputs. The first method determines the number of affine sub-models assuming known model order of the…

A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by…

We consider goal-oriented adaptive space-time finite-element discretizations of the regularized parabolic p-Laplace problem on completely unstructured simplicial space-time meshes. The adaptivity is driven by the dual-weighted residual…

We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…

We consider goal-oriented adaptive space-time finite-element discretizations of the parabolic heat equation on completely unstructured simplicial space-time meshes. In some applications, we are interested in an accurate computation of some…

This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions in two/three dimensions. The method is obtained by combining…

The thin plate spline, as introduced by Duchon, interpolates a smooth surface through scattered data. It is computationally expensive when there are many data points. The finite element thin plate spline (TPSFEM) possesses similar smoothing…

We study local approximation properties in hierarchical spline spaces through a twofold approach. First, we design and analyze a robust adaptive refinement algorithm to construct locally graded meshes. Second, we establish rigorous…

Let $\mathscr{T}$ be the regularity structure associated with a given system of singular stochastic PDEs. The paracontrolled representation of the $\sf \Pi$ map provides a linear parametrization of the nonlinear space of admissible models…

Aerodynamic optimal design is crucial for enhancing performance of aircrafts, while calculating multi-target functionals through solving dual equations with arbitrary right-hand sides remains challenging. In this paper, a novel multi-target…