Related papers: Constructing low-dimensional ordinary differential…
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…
In this paper, we solve nonlinear conservation laws using the radial basis function generated finite difference (RBF-FD) method. Nonlinear conservation laws have solutions that entail strong discontinuities and shocks, which give rise to…
Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be highly useful to deal with this problem. We describe two…
This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is…
A functional (lagged) time series regression model involves the regression of scalar response time series on a time series of regressors that consists of a sequence of random functions. In practice, the underlying regressor curve time…
For non-randomized studies, the regression discontinuity design (RDD) can be used to identify and estimate causal effects from a "locally-randomized" subgroup of subjects, under relatively mild conditions. However, current models focus…
This article develops flexible methodology to study the association between scalar outcomes and functional predictors observed over time, at many instances, in longitudinal studies. We propose a parsimonious modeling framework to study…
Fractional cumulative residual inaccuracy (FCRI) measure allows to determine regions of discrepancy between systems, depending on their respective fractional and chaotic map parameters. Most of the theoretical results and applications…
We propose a robust and computationally efficient algorithm to generically construct first return maps of dynamical systems from time series without the need for embedding. Typically, a first return map is constructed using a heuristic…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
We introduce a self-consistent deep-learning framework which, for a noisy deterministic time series, provides unsupervised filtering, state-space reconstruction, identification of the underlying differential equations and forecasting.…
We developed a novel statistical method to identify structural differences between networks characterized by structural equation models. We propose to reparameterize the model to separate the differential structures from common structures,…
An accurate vehicle dynamic model is the key to bridge the gap between simulation and real road test in autonomous driving. In this paper, we present a Dynamic model-Residual correction model Framework (DRF) for vehicle dynamic modeling. On…
The random feature method (RFM) has demonstrated great potential in bridging traditional numerical methods and machine learning techniques for solving partial differential equations (PDEs). It retains the advantages of mesh-free approaches…
Radial Basis Function-generated Finite Differences (RBF-FD) is a popular variant of local strong-form meshless methods that do not require a predefined connection between the nodes, making it easier to adapt node-distribution to the problem…
We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically…
We study semiparametric inference in some linear regression models with time-varying coefficients, dependent regressors and dependent errors. This problem, which has been considered recently by Zhang and Wu (2012) under the functional…
In this paper, a novel uncertain fractional-orders and parameters' inversion mechanism via the differential evolution algorithms (DE) with a general mathematical model is proposed for non-commensurate and hyper fractional chaotic systems.…
Quadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure between main effects…