Results 81 to 90 of about 1,345 (197)

Remarks on control and inverse problems for PDEs

SeMA Journal
Abstract This paper deals with recent results and open questions on the control and parameter identification of systems governed by PDEs. Among them, we find a few parabolic and hyperbolic equations, sometimes in the framework of a free-boundary problem. In the considered control problems, we try to govern the behavior of the solution(s) with
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Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems

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.
Cho, Sung Woong, Son, Hwijae
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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). In these problems, the goal is to find the size of the spatial interval from some appropriate boundary observations of the solution.
Apraiz, Jone, Doubova, Anna, Fernández Cara, Enrique, Yamamoto, Masahiro   +3 more
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A model-consistent data-driven computational strategy for PDE joint inversion problems

Journal of Computational Physics
The task of simultaneously reconstructing multiple physical coefficients in partial differential equations (PDEs) from observed data is ubiquitous in applications. In this work, we propose an integrated data-driven and model-based iterative reconstruction framework for such joint inversion problems where additional data on the unknown coefficients are ...
Kui Ren, Lu Zhang
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Accelerating Conjugate Gradient Solvers for Homogenization Problems With Unitary Neural Operators

International Journal for Numerical Methods in Engineering, Volume 127, Issue 5, 15 March 2026.
ABSTRACT Rapid and reliable solvers for parametric partial differential equations (PDEs) are needed in many scientific and engineering disciplines. For example, there is a growing demand for composites and architected materials with heterogeneous microstructures.
Julius Herb, Felix Fritzen
wiley   +1 more source

Breaking Barriers in High‐Order Spectral Methods: The Intrinsic Matrix Approach

International Journal for Numerical Methods in Engineering, Volume 127, Issue 5, 15 March 2026.
ABSTRACT This paper introduces a unified framework in Hilbert spaces for applying high‐order differential operators in bounded domains using Chebyshev, Legendre, and Fourier spectral methods. By exploiting the banded structure of differentiation matrices and embedding boundary conditions directly into the operator through a scaling law relating ...
Osvaldo Guimarães, José R. C. Piqueira
wiley   +1 more source

Stable Model Reduction for Time‐Domain Room Acoustics: A Structure‐Preserving Formulation for Complex Boundaries

International Journal for Numerical Methods in Engineering, Volume 127, Issue 5, 15 March 2026.
ABSTRACT This work presents novel structure‐preserving formulations for stable model order reduction in the context of time‐domain room acoustics simulations. A solution to address the instability in conventional model order reduction formulations based on the Linearized Euler Equations is derived and validated through numerical experiments.
Satish Bonthu, Hermes Sampedro Llopis, Solvi Thrastarson, Finnur Pind, Runar Unnthorsson   +4 more
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

Engineered Optical Fibers for Deep‐Tissue Applications

Advanced Optical Materials, Volume 14, Issue 10, 13 March 2026.
This review establishes a foundational framework for designing optical fibers for deep‐tissue medicine. It systematically links material innovations like polymers and hydrogels with structural paradigms to enable state‐of‐the‐art diagnostics, including endoscopy and biosensing, and targeted therapeutics, guiding future clinical translation.
Yuzhen Li, Siyang Zheng, Wenzhao Li, Kai Chen, Tianting Zhong, Chi Man Woo, Weiran Pang, Chuqi Yuan, Xiaozhou Xiao, Xianguang Yang, Long Jin, Xiang Qian, Qiyao Tan, Changyuan Yu, Liwei Liu, Junle Qu, Puxiang Lai   +16 more
wiley   +1 more source

Navigating the Ethereal Tightrope: The Nanogenerator Manipulates Neurons for Immune Equilibrium

Advanced Science, Volume 13, Issue 14, 9 March 2026.
This review explores how nanogenerators modulate neuroimmune responses, offering innovative strategies for treating neurological disorders. By interfacing with neural pathways, they enable precise control of immune activity, especially via vagus nerve stimulation.
Jia Du, Rui Deng, Ya Wu, Hong‐Xia Ren, Zong‐Hong Lin, Yang‐Bao Miao   +5 more
wiley   +1 more source