Related papers: Adaptive Refinement for Unstructured T-Splines wit…

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…

Depth refinement aims to infer high-resolution depth with fine-grained edges and details, refining low-resolution results of depth estimation models. The prevailing methods adopt tile-based manners by merging numerous patches, which lacks…

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp…

Since medical image data sets contain few samples and singular features, lesions are viewed as highly similar to other tissues. The traditional neural network has a limited ability to learn features. Even if a host of feature maps is…

This paper considers an anomaly detection problem in which a detection algorithm assigns anomaly scores to multi-dimensional data points, such as cellular networks' Key Performance Indicators (KPIs). We propose an optimization framework to…

Many important physical problems, such as fluid structure interaction or conjugate heat transfer, require numerical methods that compute boundary derivatives or fluxes to high accuracy. This paper proposes a novel alternative to calculating…

Learning-based edge detection usually suffers from predicting thick edges. Through extensive quantitative study with a new edge crispness measure, we find that noisy human-labeled edges are the main cause of thick predictions. Based on this…

Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes…

We introduce new manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes. Such splines can be used in isogeometric analysis (IGA) to represent smooth surfaces of arbitrary topology. Since prevalent…

This work introduces a locally refined version of the Adini finite element for the planar biharmonic equation on rectangular partitions with at most one hanging node per edge. If global continuity of the discrete functions is enforced, for…

The present paper provides a general formula for the dimension of spline space over T-meshes using smoothing cofactor-conformality method. And we introduce a new notion, Diagonalizable T-mesh, over which the dimension formula is only…

Optical two-dimensional (2D) coherent spectroscopy excels in studying coupling and dynamics in complex systems. The dynamical information can be learned from lineshape analysis to extract the corresponding linewidth. However, it is usually…

Recent advances in large language models (LLMs) have yielded impressive performance on various tasks, yet they often depend on high-quality feedback that can be costly. Self-refinement methods attempt to leverage LLMs' internal evaluation…

Isogeometric Analysis is a variant of the finite element method, where spline functions are used for the representation of both the geometry and the solution. Splines, particularly those with higher degree, achieve their full approximation…

The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically…

Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…

In this paper, we explore a principal way to enhance the quality of object masks produced by different segmentation models. We propose a model-agnostic solution called SegRefiner, which offers a novel perspective on this problem by…

We present a fourth-order projection method with adaptive mesh refinement (AMR) for numerically solving the incompressible Navier-Stokes equations (INSE) with subcycling in time. Our method features (i) a reformulation of INSE so that the…

Sparse keypoint matching is crucial for 3D vision tasks, yet current keypoint detectors often produce spatially inaccurate matches. Existing refinement methods mitigate this issue through alignment of matched keypoint locations, but they…

The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…