Related papers: Weighted Essentially Non-Oscillatory Shepard metho…
Common smoothness indicators used in Weighted Essentially Non\--Os\-cil\-la\-to\-ry (WENO) reconstructions [Jiang, G.S., Shu, C.W.: Efficient implementation of {Weighted} {ENO} schemes, J.\ Comput.\ Phys. \textbf{126}, 202--228 (1996)] have…
In this work we construct a high-order, single-stage, single-step positivity-preserving method for the compressible Euler equations. Space is discretized with the finite difference weighted essentially non-oscillatory (WENO) method. Time is…
Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means…
A novel regression method is introduced and studied. The procedure weights squared residuals based on their magnitude. Unlike the classic least squares which treats every squared residual equally important, the new procedure exponentially…
This paper develops the so-called Weighted Energy-Dissipation (WED) variational approach for the analysis of gradient flows in metric spaces. This focuses on the minimization of the parameter-dependent global-in-time functional of…
A novel numerical method for the estimation of large time-varying parameter (TVP) models is proposed. The updating and smoothing estimates of the TVP model are derived within the context of generalised linear least squares and through…
We introduce a novel algorithm for nonlinear processing of data gathered by an active array of sensors which probes a medium with pulses and measures the resulting waves. The algorithm is motivated by the application of array imaging. We…
A new Essentially Non-oscillatory (ENO) recovery algorithm is developed and tested in a Finite Volume method. The construction is hinged on a reformulation of the reconstruction as the solution to a variational problem. The sign property of…
Efficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid-structure interaction or shape optimization problems. In this paper, we focus…
Unevenly spaced time series are common in astronomy because of the day-night cycle, weather conditions, dependence on the source position in the sky, allocated telescope time, corrupt measurements, for example, or be inherent to the…
For large-scale point cloud processing, resampling takes the important role of controlling the point number and density while keeping the geometric consistency. % in related tasks. However, current methods cannot balance such different…
The advantage of WENO-JS5 scheme [ J. Comput. Phys. 1996] over the WENO-LOC scheme [J. Comput. Phys.1994] is that the WENO-LOC nonlinear weights do not achieve the desired order of convergence in smooth monotone regions and at critical…
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…
Continuous representations are fundamental for modeling sampled data and performing computations and numerical simulations directly on the model or its elements. To effectively and efficiently address the approximation of point clouds we…
This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of…
Singular and oscillatory functions feature in numerous applications. The high-accuracy approximation of such functions shall greatly help us develop high-order methods for solving applied mathematics problems. This paper demonstrates that…
In this paper we develop a new sixth-order finite difference central weighted essentially non-oscillatory (WENO) scheme with Z-type nonlinear weights for nonlinear degenerate parabolic equations. The centered polynomial is introduced for…
A high-order Newton multigrid method is proposed for steady-state shallow water flows in open channels with regular and irregular geometries. The method integrates a finite volume discretization with third-order weighted essentially…
Weighting methods are essential tools for estimating causal effects in observational studies, with the goal of balancing pre-treatment covariates across treatment groups. Traditional approaches pursue this objective indirectly, for example,…
As one of the most commonly seen data challenges, missing data, in particular, multiple, non-monotone missing patterns, complicates estimation and inference due to the fact that missingness mechanisms are often not missing at random, and…