Related papers: Greedy Kernel Methods for Center Manifold Approxim…

Deep neural networks are highly vulnerable to adversarial examples, which are inputs with small, carefully crafted perturbations that cause misclassification -- making adversarial attacks a critical tool for evaluating robustness. Existing…

Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engineering problems, they have not been shown, theoretically or…

This paper derives error bounds for regression in continuous time over subsets of certain types of Riemannian manifolds.The regression problem is typically driven by a nonlinear evolution law taking values on the manifold, and it is cast as…

We propose a novel supervised learning method to optimize the kernel in the maximum mean discrepancy generative adversarial networks (MMD GANs), and the kernel support vector machines (SVMs). Specifically, we characterize a distributionally…

We propose a new concept named adaptive submodularity ratio to study the greedy policy for sequential decision making. While the greedy policy is known to perform well for a wide variety of adaptive stochastic optimization problems in…

In dynamical systems theory, a fixed point of the dynamics is called nonhyperbolic if the linearization of the system around the fixed point has at least one eigenvalue with zero real part. The center manifold existence theorem guarantees…

While neural networks have demonstrated impressive performance across various tasks, accurately quantifying uncertainty in their predictions is essential to ensure their trustworthiness and enable widespread adoption in critical systems.…

This article is the updated version of the paper: "Combined 3D thinning and greedy algorithm to approximate realistic particles with corrected mechanical properties, Granular Matter (2019)" by the first author [58]. The main changes here…

The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However,…

An adaptive scheme to generate reduced-order models for parametric nonlinear dynamical systems is proposed. It aims to automatize the POD-Greedy algorithm combined with empirical interpolation. At each iteration, it is able to adaptively…

Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to…

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…

We consider how mathematical models enable predictions for conditions that are qualitatively different from the training data. We propose techniques based on information topology to find models that can apply their learning in regimes for…

Kernel-based clustering algorithms have the ability to capture the non-linear structure in real world data. Among various kernel-based clustering algorithms, kernel k-means has gained popularity due to its simple iterative nature and ease…

We analyse the performance of several iterative algorithms for the quantisation of a probability measure $\mu$, based on the minimisation of a Maximum Mean Discrepancy (MMD). Our analysis includes kernel herding, greedy MMD minimisation and…

Recently, a framework for controller design of sampled-data nonlinear systems via their approximate discrete-time models has been proposed in the literature. In this paper we develop novel tools that can be used within this framework and…

We present a technique that allows for improving on some relative greedy procedures by well-chosen (non-oblivious) local search algorithms. Relative greedy procedures are a particular type of greedy algorithm that start with a simple,…

This paper addresses a kernel-based learning problem for a network of agents locally observing a latent multidimensional, nonlinear phenomenon in a noisy environment. We propose a learning algorithm that requires only mild a priori…

We study ways to accelerate greedy coordinate descent in theory and in practice, where "accelerate" refers either to $O(1/k^2)$ convergence in theory, in practice, or both. We introduce and study two algorithms: Accelerated Semi-Greedy…

Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…