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

We introduce a novel approach for scalable domain adaptation in cloud robotics scenarios where robots rely on third-party AI inference services powered by large pre-trained deep neural networks. Our method is based on a downstream…

Digital terrain models (DTMs) are created using elevation data collected in geological surveys using varied sampling techniques like airborne lidar and depth soundings. This often leads to large data sets with different distribution…

Detecting slender, overlapping structures remains a challenge in computational microscopy. While recent coordinate-based approaches improve detection, they often produce less accurate splines than pixel-based methods. We introduce a…

This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient…

We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…

The present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order…

We introduce a new scheme adaption strategy for one- and two-dimensional hyperbolic systems of conservation laws. The proposed approach builds upon the adaptive framework introduced in [S. Chu, A. Kurganov, and I. Menshov, Appl. Numer.…

When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code…

The parameterization of open and closed anatomical surfaces is of fundamental importance in many biomedical applications. Spherical harmonics, a set of basis functions defined on the unit sphere, are widely used for anatomical shape…

Invariant-based models for incompressible isotropic hyperelasticity are typically formulated as functions of the first and second invariants, $W = W(\bar{I}_1, \bar{I}_2)$. A widely used class of models employs separable representations of…

In recent years, partial differential equation (PDE) systems have been successfully applied to the binarization of text images, achieving promising results. Inspired by the DH model and incorporating a novel image modeling approach, this…

This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…

We consider second-order PDE problems set in unbounded domains and discretized by Lagrange finite elements on a finite mesh, thus introducing an artificial boundary in the discretization. Specifically, we consider the reaction diffusion…

Excellent performance has been achieved on instance segmentation but the quality on the boundary area remains unsatisfactory, which leads to a rising attention on boundary refinement. For practical use, an ideal post-processing refinement…

In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…

We study penalization coupled with time discretization for decoupled Markovian doubly reflected BSDEs with obstacles \(p_b(t,X_t)\le Y_t\le p_w(t,X_t)\). The DRBSDE is approximated by a penalized BSDE with parameter \(\lambda\) and…

In this paper, we present a block-oriented scheme for adaptive mesh refinement based on summation-by-parts (SBP) finite difference methods and simultaneous-approximation-term (SAT) interface treatment. Since the order of accuracy at SBP-SAT…

This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block structured hierarchical…

In this work, we study the affine-constrained $\ell_1$ regularizers, which frequently arise in statistical and machine learning problems across a variety of applications, including microbiome compositional data analysis and sparse subspace…

We introduce adaptive particle refinement for compressible smoothed particle hydrodynamics (SPH). SPH calculations have the natural advantage that resolution follows mass, but this is not always optimal. Our implementation allows the user…