Results 121 to 130 of about 2,048 (231)

Numerical approximation of inverse problems for PDEs via neural network augmentation [PDF]

, 2020
LAUREA MAGISTRALEN/AIn this thesis, we consider the numerical approximation of inverse problems for linear and nonlinear elliptic PDEs by augmenting them with a neural network to predict unknown or uncertain model coefficients.
MONTAG, DILLON VICTOR PAUL
core  

Physics-Informed Neural Network solutions for nonlinear wave equations: Applications to Rosenau–Hyman and Sharma–Tasso–Olver equations

Scientific African
This study investigates the application of Physics-Informed Neural Networks (PINNs) to nonlinear dispersive wave equations, focusing on the Rosenau–Hyman (RH) and Sharma–Tasso–Olver (STO) models.
Waleed Adel, Yassine Sabbar, Kottakkaran Sooppy Nisar   +2 more
doaj   +1 more source

Chebyshev Smoothing With Adaptive Block‐FSAI Preconditioners for the Multilevel Solution of Higher‐Order Problems With the Partition of Unity Method

Numerical Linear Algebra with Applications, Volume 33, Issue 3, June 2026.
ABSTRACT In this paper, we assess the performance of adaptive and nested factorized sparse approximate inverses as smoothers in multilevel V‐cycles, when smoothing is performed following the Chebyshev iteration of the fourth kind, for the efficient solution of linear systems arising from a conforming discretization of higher‐order partial differential ...
Pablo Jiménez Recio, Marc Alexander Schweitzer   +1 more
wiley   +1 more source

Neumann problem on the semi-line for the Burgers equation

, 2011
In this article, the Neumann problem on the semi-line for the Burgers equation is considered. The problem is reduced to a nonlinear integral equation in one independent variable, whose unique solution is proven to exist for small time.
Sommacal, Matteo, de Lillo, Silvana
core   +1 more source

An Augmented Lagrangian Preconditioner for Navier–Stokes Equations With Runge–Kutta in Time

Numerical Linear Algebra with Applications, Volume 33, Issue 3, June 2026.
ABSTRACT We consider an implicit Runge–Kutta method for the numerical time integration of the nonstationary incompressible Navier–Stokes equations. This yields a sequence of nonlinear problems to be solved for the stages of the Runge–Kutta method. The resulting nonlinear system of differential equations is discretized using a finite element method.
Santolo Leveque, Yunhui He, Maxim Olshanskii   +2 more
wiley   +1 more source

Gram Decay and Intrinsic Dimensions of Krylov Subspaces

Numerical Linear Algebra with Applications, Volume 33, Issue 3, June 2026.
ABSTRACT Krylov subspace methods solve large sparse linear systems Ax=b$$ Ax=b $$ by building a sequence of polynomial approximations to A−1b$$ {A}^{-1}b $$ from successive matrix‐vector products. In finite precision, the number of numerically independent directions that can be extracted from this sequence is bounded by the intrinsic information ...
Stephen J. Thomas
wiley   +1 more source

A multi-layer neural network-based evaluation of MHD radiative heat transfer in Eyring–Powell fluid model

Heliyon
In the modern era, artificial intelligence (AI) has been applied as one of the transformative factors for scientific research in many fields that could provide new solutions to extremely complicated and complex physical models.
Muflih Alhazmi, Zahoor Shah, Muhammad Asif Zahoor Raja, Nafisa A. Albasheir, Maryam Jawaid   +4 more
doaj   +1 more source

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems

CoRR
Inverse problems involving partial differential equations (PDEs) can be seen as discovering a mapping from measurement data to unknown quantities, often framed within an operator learning approach. However, existing methods typically rely on large amounts of labeled training data, which is impractical for most real-world applications.
Sung Woong Cho, Hwijae Son
openaire   +3 more sources

Building a Digital Twin for Material Testing: Model Reduction and Data Assimilation

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.
ABSTRACT The rapid advancement of industrial technologies, data collection, and handling methods has paved the way for the widespread adoption of digital twins (DTs) in engineering, enabling seamless integration between physical systems and their virtual counterparts.
Rubén Aylwin, Nina Beranek, Gajendra Babu Budihala, Matthias Mettenleiter, Goksu Oruc, Karsten Urban   +5 more
wiley   +1 more source

Theoretical and numerical results for some inverse problems for PDEs

, 2021
We consider geometric inverse problems concerning the one-dimensional Burgers equation and some related nonlinear systems (involving heat effects and variable density).
Fernández Cara, Enrique, Doubova, Anna, Apraiz, Jone, Yamamoto, Masahiro   +3 more
core