A new implicit surface fitting method for surface reconstruction from scattered point data is proposed. The method combines an adaptive partition of unity approximation with least-squares RBF fitting and is capable of generating a high quality surface reconstruction. Given a set of points scattered over a smooth surface, first a sparse set of overlapped local approximations is constructed. The ...

Mathematical modeling of space and climate phenomena generally requires the solution of partial differential equations (PDEs) inside/outside or on a sphere. A key difficulty is that it is impossible to uniformly distribute more than 20 points on a sphere, in contrast to trivially placing any number of points uniformly along the periphery of a circle. The essence of the problem is one that has f...

The Ginzburg–Landau equation has been used as a mathematical model for various pattern formation systems in mechanics, physics and chemistry. In this paper, we study the complex Ginzburg–Landau equation in two spatial dimensions with periodical boundary conditions. The method numerically approximates the solution by collocation method based on radial basis functions (RBFs). To improve the numer...

We have applied several dimensionality reduction techniques to data modelling using neural network architectures for classification using a number of data sets. The reduction methods considered include both linear and non linear forms of principal components analysis, genetic algorithms and sensitivity analysis. The results of each were used as inputs to several types of neural network architec...

We utilize radial basis functions (RBFs) to construct numerical schemes for Hamilton–Jacobi (HJ) equations on unstructured data sets in arbitrary dimensions. The computational setup is a meshless discretization of the physical domain. We derive monotone schemes on unstructured data sets to compute the viscosity solutions. The essentially nonoscillatory (ENO) mechanism is combined with radial ba...

Motivated by the fractal-like behavior of natural images, we propose a new smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional has previously been introduced by Duchon in the context of radial basis functions (RBFs) for the approximation of non-uniform data. Here, we introduce a new solution to Duchon’s smoothing prob...

In this paper we evaluate two Temporal Difference Reinforcement Learning methods on several different tasks to see how well these methods generalize. The tasks were modeled as Markov Decision Processes with a continuous observation space and a discrete action space. Function approximation was done using linear gradient descent with RBFs as features. The tasks were taken from the Polyathlon doma...

This paper describes a parametric optimization technique for shape and topology optimization. The proposed method is a generalization of the classical method of level sets which are represented with discrete grids. In using radial basis functions (RBFs), the proposed formulation projects the geometric motion of the level sets of an implicit function onto its parametric representation. The resul...

Using multilayer perceptrons (MLPs) to approximate the state-action value function in reinforcement learning (RL) algorithms could become a nightmare due to the constant possibility of unlearning past experiences. Moreover, since the target values in the training examples are bootstraps values, this is, estimates of other estimates, the chances to get stuck in a local minimum are increased. The...

In this paper, a technique generally known as meshless method is presented for solving fractional partial differential equations (FPDEs). Some physical linear and nonlinear experiments such as time-fractional convective-diffusion equation, timefractional wave equation and nonlinear space-fractional Fisher's equation are considered. We present the advantages of using the radial basis functions (...