相关论文: SoftIGA: soft isogeometric analysis

Algebraic Multigrid (AMG) methods are state-of-the-art algebraic solvers for partial differential equations. Still, their efficiency depends heavily on the choice of suitable parameters and/or ingredients. Paradigmatic examples include the…

In this contribution, we provide a new mass lumping scheme for explicit dynamics in isogeometric analysis (IGA). To this end, an element formulation based on the idea of dual functionals is developed. Non-Uniform Rational B-splines (NURBS)…

We propose a randomized first order optimization method--SEGA (SkEtched GrAdient method)-- which progressively throughout its iterations builds a variance-reduced estimate of the gradient from random linear measurements (sketches) of the…

We describe and analyze algorithms for shape-constrained symbolic regression, which allows the inclusion of prior knowledge about the shape of the regression function. This is relevant in many areas of engineering -- in particular whenever…

In this paper, we introduce the isoGeometric Residual Minimization (iGRM) method. The method solves stationary advection-dominated diffusion problems. We stabilize the method via residual minimization. We discretize the problem using…

Soft threshold pruning is among the cutting-edge pruning methods with state-of-the-art performance. However, previous methods either perform aimless searching on the threshold scheduler or simply set the threshold trainable, lacking…

Over the past ten years, driven by large scale optimisation problems arising from machine learning, the development of stochastic optimisation methods have witnessed a tremendous growth. However, despite their popularity, the theoretical…

We study a higher-order surface finite element (SFEM) penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated which are equivalent in the continuous setting. The impact of the…

Subsea umbilical and power cables contain a large number of contact interfaces between different geometries and materials. These complex interactions rise significant challenges for accurately considering contact surface properties by using…

In Part II of this two-part paper, we prove the convergence of the simplified information geometry approach (SIGA) proposed in Part I. For a general Bayesian inference problem, we first show that the iteration of the common second-order…

We construct and analyze a TraceFEM discretization for the surface biharmonic problem. The method utilizes standard quadratic Lagrange finite element spaces defined on a three-dimensional background mesh and a symmetric $C^0$ interior…

Gradient descent can be surprisingly good at optimizing deep neural networks without overfitting and without explicit regularization. We find that the discrete steps of gradient descent implicitly regularize models by penalizing gradient…

This work develops a numerical solver based on the combination of isogeometric analysis (IGA) and the tensor train (TT) decomposition for the approximation of partial differential equations (PDEs) on parameter-dependent geometries. First,…

We present a robust and efficient multigrid method for single-patch isogeometric discretizations using tensor product B-splines of maximum smoothness. Our method is based on a stable splitting of the spline space into a large subspace of…

This work presents an efficient quadrature rule for shell analysis fully integrated in CAD by means of Isogeometric Analysis (IGA). General CAD-models may consist of trimmed parts such as holes, intersections, cut-offs etc. Therefore, IGA…

Despite the rise to fame of incremental variance-reduced methods in recent years, their use in nonsmooth optimization is still limited to few simple cases. This is due to the fact that existing methods require to evaluate the proximity…

Federated Learning (FL) enables collaborative model training across decentralized edge devices while preserving data privacy. However, statistical heterogeneity among clients, often manifested as non-IID label distributions, poses…

The Shallow Ice Approximation (SIA) model on strong form is commonly used for inferring the flow dynamics of grounded ice sheets. The solution to the SIA model is a closed-form expression for the velocity field. When that velocity field is…

Faster inference of deep learning models is highly demanded on edge devices and even servers, for both financial and environmental reasons. To address this issue, we propose SoftNeuro, a novel, high-performance inference framework with…

We develop a multigrid solver for the second biharmonic problem in the context of Isogeometric Analysis (IgA), where we also allow a zero-order term. In a previous paper, the authors have developed an analysis for the first biharmonic…