Related papers: Greedy Kernel Methods for Approximating Breakthrou…

Active learning is increasingly adopted for expensive multi-objective combinatorial optimization problems, but it involves a challenging subset selection problem, optimizing the batch acquisition score that quantifies the goodness of a…

Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms…

We propose a new method for learning deep neural network models that is based on a greedy learning approach: we add one basis function at a time, and a new basis function is generated as a non-linear activation function applied to a linear…

We propose a probabilistic shape completion method extended to the continuous geometry of large-scale 3D scenes. Real-world scans of 3D scenes suffer from a considerable amount of missing data cluttered with unsegmented objects. The problem…

Simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment related activities. The numerical simulators used for modeling such processes rely on spatial and temporal…

We consider the approximation capability of orthogonal super greedy algorithms (OSGA) and its applications in supervised learning. OSGA is concerned with selecting more than one atoms in each iteration step, which, of course, greatly…

We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…

3D action recognition was shown to benefit from a covariance representation of the input data (joint 3D positions). A kernel machine feed with such feature is an effective paradigm for 3D action recognition, yielding state-of-the-art…

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…

Modeling effective transport properties of 3D porous media, such as permeability, at multiple scales is challenging as a result of the combined complexity of the pore structures and fluid physics - in particular, confinement effects which…

The accuracy of coarse-grained continuum models of dense granular flows is limited by the lack of high-fidelity closure models for granular rheology. One approach to addressing this issue, referred to as the hierarchical multiscale method,…

Fluid flow through intricate confining geometries often exhibits complex behaviors, certainly in porous materials, e.g. in groundwater flows or the operation of filtration devices and porous catalysts. However, it has remained extremely…

Pretraining molecular representation models without labels is fundamental to various applications. Conventional methods mainly process 2D molecular graphs and focus solely on 2D tasks, making their pretrained models incapable of…

3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior…

This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…

In this work, we use a moving Voronoi and sharp interface approach for simulating two-phase flows. At every time step, the mesh is generated anew from Voronoi seeds that behave as material points. The paper is a continuation of our previous…

Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…

The computation of (i) $\varepsilon$-kernels, (ii) approximate diameter, and (iii) approximate bichromatic closest pair are fundamental problems in geometric approximation. In this paper, we describe new algorithms that offer significant…

We present an integrated approach for the use of simulated data from full order discretization as well as projection-based Reduced Basis reduced order models for the training of machine learning approaches, in particular Kernel Methods, in…

Hemodynamic quantities are valuable biomedical risk factors for cardiovascular pathology such as atherosclerosis. Non-invasive, in-vivo measurement of these quantities can only be performed using a select number of modalities that are not…