Related papers: A Kernel-based Lagrangian Method for Imperfectly-m…
A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…
We introduce a nonparametric algorithm to learn interaction kernels of mean-field equations for 1st-order systems of interacting particles. The data consist of discrete space-time observations of the solution. By least squares with…
The immersed boundary (IB) method is a general mathematical framework for studying problems involving fluid-structure interactions in which an elastic structure is immersed in a viscous incompressible fluid. In the IB formulation, the fluid…
A significant drawback of Lagrangian (particle-tracking) reactive transport models has been their inability to properly simulate interactions between solid and liquid chemical phases, such as dissolution and precipitation reactions. This…
We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a…
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…
Local polynomial density (LPD) estimators are widely used for inference on boundary features of the density function. Contrary to conventional wisdom, we show that kernel choice substantially affects efficiency. Theory, simulations, and…
A dilute system of reacting particles transported by fluid flows is considered. The particles react as $A + A \to \varnothing$ with a given rate when they are within a finite radius of interaction. The system is described in terms of the…
In this work, we present a high-fidelity and efficient point-particle direct numerical simulation framework based on a multi-block overset curvilinear grid system, enabling large-scale Lagrangian particle tracking in complex geometries with…
We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…
Several Lagrangian methodologies have been proposed in recent years to simulate advection-dispersion of solutes in fluids as a mass exchange between numerical particles carrying the fluid. In this paper, we unify these methodologies,…
It is well-known that polynomial reproduction is not possible when approximating with Gaussian kernels. Quasi-interpolation schemes have been developed which use a finite number of Gaussians at different scales, which then reproduce…
Many scientific problems require identifying a small set of covariates that are associated with a target response and estimating their effects. Often, these effects are nonlinear and include interactions, so linear and additive methods can…
The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…
In this paper, we develop a quadrature framework for large-scale kernel machines via a numerical integration representation. Considering that the integration domain and measure of typical kernels, e.g., Gaussian kernels, arc-cosine kernels,…
We consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by…
Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…
The advantage of particle Lagrangian methods in computational fluid dynamics is that advection is accurately modeled. However, this complicates the calculation of space derivatives. If a mesh is employed, it must be updated at each time…
One of the main challenges in diffusion-based molecular communication is dealing with the non-linearity of reaction-diffusion chemical equations. While numerical methods can be used to solve these equations, a change in the input signals or…
Ab initio quantum chemical methods for accurately computing interactions between molecules have a wide range of applications but are often computationally expensive. Hence, selecting an appropriate method based on accuracy and computational…