Related papers: A meshless and binless approach to compute statist…

Kernel smooth is the most fundamental technique for data density and regression estimation. However, time-consuming is the biggest obstacle for the application that the direct evaluation of kernel smooth for $N$ samples needs ${O}\left(…

In this work, we present a computationally efficient methodology that utilizes a local real-space formulation of the projector augmented wave (PAW) method discretized with a finite-element (FE) basis to enable accurate and large-scale…

Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for…

This thesis explores parameter estimation methods for rapidly reconstructing compact binary sources generating gravitational waves. It employs numerical linear algebra and meshfree approximation techniques to expedite waveform generation…

Bolted joints can exhibit nonsmooth and significantly nonlinear dynamics. Finite Element Models (FEMs) of this phenomenon require fine spatial discretizations, inclusion of nonlinear contact and friction laws, as well as geometric…

We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex,…

This paper aims to survey our recent work relating to the radial basis function (RBF) and its applications to numerical PDEs. We introduced the kernel RBF involving general pre-wavelets and scale-orthogonal wavelets RBF. A…

A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over the volume of the ball in three dimensions is described. Such methods are necessary in many areas of Applied…

Ensemble methods are among the state-of-the-art predictive modeling approaches. Applied to modern big data, these methods often require a large number of sub-learners, where the complexity of each learner typically grows with the size of…

Unimodality constitutes a key property indicating grouping behavior of the data around a single mode of its density. We propose a method that partitions univariate data into unimodal subsets through recursive splitting around valley points…

One of the most popular methods employed in computational electromagnetics is the Finite Difference Time Domain (FDTD) method. We generalise it to a meshless setting using the Radial Basis Function generated Finite Difference (RBF-FD)…

This article reports on the efficiency of a co-located diffuse approximation method coupled with a projection algorithm for the solution of two and three-dimensional incompressible flow equations. Three typical examples show the accuracy of…

This study introduces a framework for the forecasting, reconstruction and feature engineering of multivariate processes along with its renewable energy applications. We integrate derivative-free optimization with an ensemble of…

This article proposes a novel high-performance computing approach for the prediction of the temperature field in powder bed fusion (PBF) additive manufacturing processes. In contrast to many existing approaches to part-scale simulations,…

A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for…

The paper introduces a new meshfree pseudospectral method based on Gaussian radial basis functions (RBFs) collocation to solve fractional Poisson equations. Hypergeometric functions are used to represent the fractional Laplacian of Gaussian…

The finite difference time domain method is one of the simplest and most popular methods in computational electromagnetics. This work considers two possible ways of generalising it to a meshless setting by employing local radial basis…

We present a fast Bayesian inference framework to address the growing computational cost of gravitational-wave parameter estimation. The increased cost is driven by improved broadband detector sensitivity, particularly at low frequencies…

Event-based vision encodes dynamic scenes as asynchronous spatio-temporal spikes called events. To leverage conventional image processing pipelines, events are typically binned into frames. However, binning functions are discontinuous,…

Physics-informed neural networks (PINNs) have lately received significant attention as a representative deep learning-based technique for solving partial differential equations (PDEs). Most fully connected network-based PINNs use automatic…