Results 201 to 210 of about 37,100 (232)

BiLO: Bilevel Local Operator Learning for PDE Inverse Problems

bioRxiv
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, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub   +3 more
semanticscholar   +3 more sources

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Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

IMA Journal of Numerical Analysis, 2020
Physics-informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for partial differential equations (PDEs).
Siddhartha Mishra, R. Molinaro
semanticscholar   +1 more source

Correction to: Remarks on control and inverse problems for PDEs

SeMA Journal
Enrique Fernández-Carawas
semanticscholar   +2 more sources

PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

SIAM Journal on Scientific Computing, 2022
This paper deals with solving an inverse problem of electrocardiography involving deep learning (DL). In more detail: ``The goal of this work is to show how the integration between DL techniques and physically based regularization allows one to accurately solve the inverse problem of electrocardiography, even in a small data regime.'' (page B608).
Riccardo Tenderini, Stefano Pagani, Alfio Quarteroni, Simone Deparis   +3 more
openaire   +2 more sources

Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators

Inverse Problems, 2022
This paper deals with direct and inverse source problems for parabolic or byperbolic PDEs containing nonlinear Volterra operators (including the variable order time-fractional derivatives).
M. Slodicka
semanticscholar   +1 more source

The Gradient Descent Method for the Convexification to Solve Boundary Value Problems of Quasi-Linear PDEs and a Coefficient Inverse Problem

Journal of Scientific Computing, 2021
We study the global convergence of the gradient descent method of the minimization of strictly convex functionals on an open and bounded set of a Hilbert space.
T. Le, L. Nguyen
semanticscholar   +1 more source

Numerical Solution Of Inverse Problem For Elliptic Pdes

International Journal of Computer Mathematics, 2003
This work is concerned with computing the solution of the following inverse problem: Finding u and „on D such that: $$\nabla \cdot (\rho \nabla u) = 0,\quad \hbox{on}\ D;$$ $$u = g,\quad \hbox{on}\ \partial D;\qquad \rho u_n = f,\quad \hbox{on}\ \partial D;$$ $$\rho (x_0, y_0) = \rho_0,\quad \hbox{for a given point}\ (x_0, y_0) \in D$$ where f and g ...
Ali Sayfy, Sadia Makky
openaire   +1 more source

Deep Learning for PDE-based Inverse Problems

Oberwolfach Reports
Workshop ...
Simon Arridge, Peter Maaß, Carola-Bibiane Schönlieb   +2 more
openaire   +2 more sources

Kernel-Adaptive PI-ELMs for Forward and Inverse Problems in PDEs with Sharp Gradients

arXiv.org
Physics-informed machine learning frameworks such as Physics-Informed Neural Networks (PINNs) and Physics-Informed Extreme Learning Machines (PI-ELMs) have shown great promise for solving partial differential equations (PDEs) but struggle with localized ...
Vikas Dwivedi, Balaji Srinivasan, Monica Sigovan, Bruno Sixou   +3 more
semanticscholar   +1 more source

Uncertainty Quantification for Forward and Inverse Problems of PDEs via Latent Global Evolution

AAAI Conference on Artificial Intelligence
Deep learning-based surrogate models have demonstrated remarkable advantages over classical solvers in terms of speed, often achieving speedups of 10 to 1000 times over traditional partial differential equation (PDE) solvers.
Tailin Wu, Willie Neiswanger, Hongtao Zheng, Stefano Ermon, J. Leskovec   +4 more
semanticscholar   +1 more source