相关论文: IGA-based Multi-Index Stochastic Collocation for r…

\Multiple imputation (MI) is a popular and well-established method for handling missing data in multivariate data sets, but its practicality for use in massive and complex data sets has been questioned. One such data set is the Panel Study…

Image quality assessment (IQA) is an important research topic for understanding and improving visual experience. The current state-of-the-art IQA methods are based on convolutional neural networks (CNNs). The performance of CNN-based models…

This work focuses on an efficient stress recovery procedure for laminated composite curved structures, which relies on Isogeometric Analysis (IGA) and equilibrium. Using a single element through the thickness in combination with a…

A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of…

This paper focuses on the spectral properties of the mass and stiffness matrices for acoustic wave problems discretized with Isogeometric analysis (IGA) collocation methods in space and Newmark methods in time. Extensive numerical results…

Modern control theory provides us with a spectrum of methods for studying the interconnection of dynamic systems using input-output properties of the interconnected subsystems. Perhaps the most advanced framework for such input-output…

In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on NURBS. The motivation for this work is an integrated and complete work pipeline from CAD to parametrization of domain geometry, then…

We present and analyze a stable space-time multi-patch discontinuous Galerkin Isogeometric Analysis (dG-IgA) scheme for the numerical solution of parabolic evolution equations in moving space-time computational domains. Following…

In recent publications, the author and his coworkers have proposed a multigrid method for solving linear systems arizing from the discretization of partial differential equations in isogeometric analysis and have proven that the convergence…

Independent component analysis (ICA) is a widespread data exploration technique, where observed signals are modeled as linear mixtures of independent components. From a machine learning point of view, it amounts to a matrix factorization…

A challenge in multivariate problems with discrete structures is the inclusion of prior information that may differ in each separate structure. A particular example of this is seismic amplitude versus angle (AVA) inversion to elastic…

We propose a numerical scheme based on the principles of Isogeometric Analysis (IgA) for a geometrical pattern formation induced evolution of manifolds. The development is modelled by the use of the Gray-Scott equations for pattern…

We propose an Isogeometric approach for smoothing on surfaces, namely estimating a function starting from noisy and discrete measurements. More precisely, we aim at estimating functions lying on a surface represented by NURBS, which are…

In the design of electromagnetic devices the accurate representation of the geometry plays a crucial role in determining the device performance. For accelerator cavities, in particular, controlling the frequencies of the eigenmodes is…

Stochastic partial differential equations (SPDEs) are often difficult to solve numerically due to their low regularity and high dimensionality. These challenges limit the practical use of computer-aided studies and pose significant barriers…

Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems, but they are still trapped in training failures when the target functions to be approximated exhibit…

Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discretization. By leveraging Gaussian process regression and…

Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic…

Although the isogeometric collocation (IGA-C) method has been successfully utilized in practical applications due to its simplicity and efficiency, only a little theoretical results have been established on the numerical analysis of the…

This manuscript develops a new framework to analyze and design iterative optimization algorithms built on the notion of Integral Quadratic Constraints (IQC) from robust control theory. IQCs provide sufficient conditions for the stability of…