Results 221 to 230 of about 2,057 (240)

ON AN INVERSE PROBLEM IN GROUP ANALYSIS OF PDE'S: LIE–REMARKABLE EQUATIONS

Waves and Stability in Continuous Media, 2006
Within the framework of inverse Lie problems we give some non–trivial examples of Lie–remarkable equations, i.e., classes of partial differential equations that are in one–to–one correspondence with their Lie point symmetries. In particular, we prove that the second order Monge-Ampere equation in two independent variables is Lie–remarkable.
F. OLIVERI, MANNO, GIOVANNI, VITOLO, Raffaele   +2 more
openaire   +3 more sources

Deep Learning for PDE-based Inverse Problems

Oberwolfach Reports
Workshop ...
Simon Arridge, Peter Maaß, Carola-Bibiane Schönlieb   +2 more
  +4 more sources

Geometric Methods in Inverse Problems and PDE Control

2004
Foreword * Preface * On the construction of isospectral manifolds, Werner Ballman * Statistical stability and time-reversal imaging in random media, James G. Berryman, Liliana Borcea, George C. Papanicolaou, and Chrysoul Tsogka * A review of selected works on crack identification, Kurt Bryan and Michael S.
Croke, Christopher B., Lasiecka, Irena, Uhlmann, Gunther, Vogelius, Michael S.   +3 more
openaire   +2 more sources

Solving inverse problems in nonlinear PDEs by recurrent neural networks

IEEE International Conference on Neural Networks, 2002
A neural network approach for solving inverse problems in nonlinear partial differential equations (PDEs) is proposed, and a computer simulation based on this approach is described. The network is designed based on the differential difference equation (DDE) approximating the PDE.
Tadasu Uchiyama, Noboru Sonehara
openaire   +1 more source

Fredholm Neural Networks for inverse problems in elliptic PDEs

Building on our previous work on Fredholm Neural Networks (Fredholm NNs/ FNNs) for solving integral equations, we extend the framework to inverse problems for linear and nonlinear elliptic partial differential equations. The proposed scheme consists of a custom-designed deep neural network (DNN) in which the number of layers, weights, biases and ...
Georgiou, Kyriakos C., Siettos, Constantinos, Yannacopoulos, Athanasios N.   +2 more
openaire   +1 more source

Completeness of the products of solutions of PDE and inverse problems

Inverse Problems, 1990
The author discusses the characterisation problem in 3D inverse scattering theory, an inverse spectral problem, and an inverse problem for the wave equation.
openaire   +1 more source

hIPPYlib

ACM Transactions on Mathematical Software, 2021
Umberto Villa, Noémi Petra, Omar Ghattas   +2 more
exaly  

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

IMA Journal of Numerical Analysis, 2022
Siddhartha Mishra, Roberto Molinaro, Mishra Siddhartha   +2 more
exaly  

Generalized conditional symmetry enhanced physics-informed neural network and application to the forward and inverse problems of nonlinear diffusion equations

Chaos, Solitons and Fractals, 2023
Zhi-Yong Zhang
exaly  

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

Inverse Problems, 2022
Marian Slodička
exaly