Results 231 to 240 of about 35,710 (245)

E-PINN: extended physics informed neural network for the forward and inverse problems of high-order nonlinear integro-differential equations

International Journal of Computational Mathematics
Physics informed neural network (PINN) is a new deep learning paradigm, which embeds the physical information delineated by PDEs in the loss function and optimizes the weights in the neural network.
HongMing Zhang, Xinping Shao, Zhengfang Zhang, Mingyan He   +3 more
semanticscholar   +1 more source

VC-PINN: Variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficient

Physica A: Statistical Mechanics and its Applications, 2023
Zhengwu Miao, Yong Chen
semanticscholar   +1 more source

A gaussian process framework for solving forward and inverse problems involving nonlinear partial differential equations

Computational Mechanics
Physics-informed machine learning (PIML) has emerged as a promising alternative to conventional numerical methods for solving partial differential equations (PDEs).
Carlos Mora, Amin Yousefpour, Shirin Hosseinmardi, R. Bostanabad   +3 more
semanticscholar   +1 more source

BiLO: Bilevel Local Operator Learning for PDE inverse problems

arXiv.org
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem.
Ray Zirui Zhang, Xiaohui Xie, John S. Lowengrub   +2 more
semanticscholar   +1 more source

Weak neural variational inference for solving Bayesian inverse problems without forward models: applications in elastography

Computer Methods in Applied Mechanics and Engineering
In this paper, we introduce a novel, data-driven approach for solving high-dimensional Bayesian inverse problems based on partial differential equations (PDEs), called Weak Neural Variational Inference (WNVI).
Vincent C. Scholz, Yaohua Zang, P. Koutsourelakis   +2 more
semanticscholar   +1 more source

Physics-informed neural networks for inverse problems in structural dynamics

Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring
This study introduces an innovative approach that employs Physics-Informed Neural Networks (PINNs) to address inverse problems in structural analysis.
Rafael de O. Teloli, Mael Bigot, Lucas Coelho, Emmanuel Ramasso, Roberta Tittarelli, Patrice Le Moal, M. Ouisse   +6 more
semanticscholar   +1 more source

Quasi-Monte Carlo for Bayesian design of experiment problems governed by parametric PDEs

arXiv.org
This paper contributes to the study of optimal experimental design for Bayesian inverse problems governed by partial differential equations (PDEs). We derive estimates for the parametric regularity of multivariate double integration problems over high ...
V. Kaarnioja, C. Schillings
semanticscholar   +1 more source

Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equations

arXiv.org
Physics-informed neural networks (PINNs) represent a significant advancement in scientific machine learning by integrating fundamental physical laws into their architecture through loss functions.
Wei Zhou, Y. F. Xu
semanticscholar   +1 more source

Robust optimal design of large-scale Bayesian nonlinear inverse problems

arXiv.org
We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse ...
Abhijit Chowdhary, Ahmed Attia, A. Alexanderian   +2 more
semanticscholar   +1 more source

Some non-linear systems of PDEs related to inverse problems in conductivity

Calculus of Variations and Partial Differential Equations, 2021
Faustino Maestre, P. Pedregal
semanticscholar   +1 more source