Related papers: An adaptive kernel-split quadrature method for par…

In this paper, Bayesian optimisation is used to simultaneously search the optimal values of the shape parameter and the radius in radial basis function partition of unity interpolation problem. It is a probabilistic iterative approach that…

In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the…

Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…

Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…

Structured pruning compresses neural networks by reducing channels (filters) for fast inference and low footprint at run-time. To restore accuracy after pruning, fine-tuning is usually applied to pruned networks. However, too few remaining…

This paper presents a method for the approximation of harmonic potentials that combines downward continuation of globally available data on a sphere $\Omega_R$ of radius $R$ (e.g., a satellite's orbit) with locally available data on a…

Quadrature by Expansion (QBX) is a quadrature method for approximating the value of the singular integrals encountered in the evaluation of layer potentials. It exploits the smoothness of the layer potential by forming locally-valid…

The inverse source problem for the Helmholtz equation poses significant challenges, particularly when sources exhibit complex or discontinuous geometries. Traditional numerical methods suffer from prohibitive computational costs, while…

The field of quantum machine learning is a promising way to lead to a revolution in intelligent data processing methods. In this way, a hybrid learning method based on classic kernel methods is proposed. This proposal also requires the…

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior…

Quadrature formulas for spheres, the rotation group, and other compact, homogeneous manifolds are important in a number of applications and have been the subject of recent research. The main purpose of this paper is to study coordinate…

Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics and machine learning. This paper proposes a weighted…

Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause…

We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…

Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We…

With the continued scaling of quantum processors, holistic benchmarks are essential for extensively evaluating device performance. Layer fidelity is a benchmark well-suited to assessing processor performance at scale. Key advantages of this…

Variational phase-field models of brittle fracture pose a local constrained minimization problem of a non-convex energy functional. In the discrete setting, the problem is most often solved by alternate minimization, exploiting the separate…

We present a fast, adaptive multiresolution algorithm for applying integral operators with a wide class of radially symmetric kernels in dimensions one, two and three. This algorithm is made efficient by the use of separated representations…

Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection…

A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the…