Results 21 to 30 of about 35,012 (233)

The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses

Examples and Counterexamples
This paper presents the Hadamard-Physics-Informed Neural Network (H-PINN) for solving inverse problems in partial differential equations (PDEs), specifically the heat equation and the Korteweg–de Vries (KdV) equation.
Yohan Chandrasukmana, Helena Margaretha, Kie Van Ivanky Saputra   +2 more
doaj   +2 more sources

CUQIpy: II. Computational uncertainty quantification for PDE-based inverse problems in Python [PDF]

Inverse Problems
Abstract Inverse problems, particularly those governed by Partial Differential Equations (PDEs), are prevalent in various scientific and engineering applications, and uncertainty quantification (UQ) of solutions to these problems is essential for informed decision-making.
Amal Alghamdi, Nicolai A. B. Riis, Babak Maboudi Afkham, Felipe Uribe, Silja Westphal Christensen, Per Christian Hansen, Jakob Sauer Jørgensen   +6 more
openalex   +5 more sources

Structured Random Sketching for PDE Inverse Problems [PDF]

SIAM Journal on Matrix Analysis and Applications, 2020
For an overdetermined system $\mathsf{A}\mathsf{x} \approx \mathsf{b}$ with $\mathsf{A}$ and $\mathsf{b}$ given, the least-square (LS) formulation $\min_x \, \|\mathsf{A}\mathsf{x}-\mathsf{b}\|_2$ is often used to find an acceptable solution $\mathsf{x}$.
Ke Chen, Qin Li, Kit Newton, Stephen J. Wright   +3 more
openaire   +3 more sources

Enhancing Computational Accuracy in Surrogate Modeling for Elastic–Plastic Problems by Coupling S-FEM and Physics-Informed Deep Learning

Mathematics, 2023
Physics-informed neural networks (PINNs) provide a new approach to solving partial differential equations (PDEs), while the properties of coupled physical laws present potential in surrogate modeling.
Meijun Zhou, Gang Mei, Nengxiong Xu
doaj   +1 more source

Inverse coefficient problem for differential equation in partial derivatives of a fourth order in time with integral over-determination

Қарағанды университетінің хабаршысы. Математика сериясы, 2022
Derivatives in time of higher order (more than two) arise in various fields such as acoustics, medical ultrasound, viscoelasticity and thermoelasticity.
M.J. Huntul, I. Tekin
doaj   +1 more source

PINNs algorithm and its application in geotechnical engineering

Yantu gongcheng xuebao, 2021
The physical information neural networks (PINNs) algorithm, a new mesh-free algorithm, uses the automatic differential method to embed the partial differential equation directly into the neural networks so as to realize the intelligent solution of the ...
LAN Peng 1, LI Hai-chao 1, YE Xin-yu 1, ZHANG Sheng 1, SHENG Dai-chao 1, 2
doaj   +1 more source

A deep neural network approach for parameterized PDEs and Bayesian inverse problems

Machine Learning: Science and Technology, 2023
We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such problems.
Harbir Antil, Howard C Elman, Akwum Onwunta, Deepanshu Verma   +3 more
doaj   +1 more source

An efficient algorithm for some highly nonlinear fractional PDEs in mathematical physics. [PDF]

PLoS ONE, 2014
In this paper, a fractional complex transform (FCT) is used to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and subsequently Reduced Differential Transform Method (RDTM) is ...
Jamshad Ahmad, Syed Tauseef Mohyud-Din
doaj   +1 more source

Modeling a Typical Non-Uniform Deformation of Materials Using Physics-Informed Deep Learning: Applications to Forward and Inverse Problems

Applied Sciences, 2023
Numerical methods, such as finite element or finite difference, have been widely used in the past decades for modeling solid mechanics problems by solving partial differential equations (PDEs).
Yawen Deng, Changchang Chen, Qingxin Wang, Xiaohe Li, Zide Fan, Yunzi Li   +5 more
doaj   +1 more source

FDM data driven U-Net as a 2D Laplace PINN solver

Scientific Reports, 2023
Efficient solution of partial differential equations (PDEs) of physical laws is of interest for manifold applications in computer science and image analysis. However, conventional domain discretization techniques for numerical solving PDEs such as Finite
Anto Nivin Maria Antony, Narendra Narisetti, Evgeny Gladilin   +2 more
doaj   +1 more source