Results 101 to 110 of about 85,369,012 (181)

Neural Adjoint Inverse Design of Three‐Dimensional Nanophotonic Devices

Nanophotonics, Volume 15, Issue 20, 27 October 2026.
A stage‐wise Fourier neural operator is trained on FDTD adjoint gradients of volumetric meta‐optics, each stage refining residuals under progressively enlarged Fourier‐mode cutoffs. Given any permittivity volume, the model reconstructs the 3D gradient field, from coarse envelope to resonance peaks, within a second, driving inverse design to 86–99% of ...
Chanik Kang, Hyewon Suk, Ikbeom Jang, Haejun Chung   +3 more
wiley   +1 more source

From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing

Mathematics
This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation. The work analyzes key models, including DeepONet,
Prashant K. Jha
doaj   +1 more source

A Unified Block‐Modal Framework for Inverse Source Problems in Heat and Mass Transfer

International Journal for Numerical Methods in Engineering, Volume 127, Issue 19, 15 October 2026.
ABSTRACT This work presents a unified block–modal framework for inverse source identification in linear diffusive problems arising in heat and mass transfer. Starting from a general parabolic model with mixed boundary operators, the Classical Integral Transform Technique is employed to project the dynamics onto an orthonormal eigenbasis, yielding a ...
André J. P. de Oliveira, Diego C. Knupp, Lucas L. S. Costa, Luiz A. S. Abreu, Mousa J. Huntul, Antônio J. Silva Neto   +5 more
wiley   +1 more source

Bi-level iterative regularization for inverse problems in nonlinear PDEs [PDF]

We investigate the ill-posed inverse problem of recovering unknown spatially dependent parameters in nonlinear evolution PDEs. We propose a bi-level Landweber scheme, where the upper-level parameter reconstruction embeds a lower-level state approximation.
Nguyen, Tram Thi Ngoc, Nguyen, T.
core   +1 more source

One-Dimensional Elastic and Viscoelastic Full-Waveform Inversion in Heterogeneous Media Using Physics-Informed Neural Networks

IEEE Access
In this study, we discuss a mathematical framework to handle the inverse problem for the applications of partial differential equations (PDEs). In particular, we focus on wave equations and attempt to identify the wave parameters such as wave velocity ...
Alireza Pakravan
doaj   +1 more source

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

Solving inverse problems for PDEs in terms of Lax-Milgram functional and a generalized collage method

In this paper, we develop a general collage coding framework for inverse problems in partial differential equations (PDEs) with boundary conditions. Although a general PDEs inverse problem can be very complicated, via the Generalized Collage Theorem in ...
Davide La Torre, Ed Vrscay, Herb Kunze
core  

Using Physics-Informed Neural Networks for Solving 2^nd-Order Volterra Integro-Differential Equation by DeepXDE Library

مجلة بغداد للعلوم
Many disciplines widely use deep learning (DL) as a key tool for investigating the behavior of various systems. Deep learning (DL) has recently been utilized to solve differential equations using physics-based input.
Oday Ahmed Jasim, Abdulghafor M. Al-Rozbayani   +1 more
doaj   +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

Inverse problems for quantum trees

, 2008
Three different inverse problems for the Schrodinger operator on a metric tree are considered, so far with standard boundary conditions at the vertices.
Avdonin, Sergei, Kurasov, Pavel,
core