This volume contains the proceedings of two AMS Special Sessions ""Recent Developments on Analysis and Computation for Inverse Problems for PDEs"", virtually held on March 13-14, 2021, and ""Recent Advances in Inverse Problems for Partial Differential Equations"",' virtually held on October 23-24, 2021.
The papers in this volume focus on new results on numerical methods for various inverse problems arising in electrical impedance tomography, inverse scattering in radar and optics problems, reconstruction of initial conditions, control of acoustic fields, and stock price forecasting. The authors studied iterative and non-iterative approaches such as optimization-based, globally convergent, sampling, and machine learning-based methods.
The volume provides an interesting source on advances in computational inverse problems for partial differential equations.
U. G. Abdulla and S. Seif, Discretization and convergence of the EIT
optimal control problem in Sobolev spaces with dominating mixed smoothness
T. T. Le, Global reconstruction of initial conditions of nonlinear parabolic
equations via the Carleman-contraction method
I. Harris, Regularization of the factorization method with applications to
inverse scattering
T. Le, D.-L. Nguyen, V. Nguyen, and T. Truong, Sampling type method combined
with deep learning for inverse scattering with one incident wave
D.-L. Nguyen and T. Truong, Fast numerical solutions to direct and inverse
scattering for bi-anisotropic periodic Maxwell's equation
L. H. Nguyen and H. T.T. Vu, Reconstructing a space-dependent source term via
the quasi-reversibility method
Q. Tran, Convergence analysis of Nedelec finite element approximations for a
stationary Maxwell's system
M. V. Klibanov, K. V. Golubnichiy, and A. V. Nikitin, Quasi-reversibility
method and neural network machine learning for forecasting of stock option
prices
V. A. Khoa, M. V. Klibanov, W. G. Powell, and L. C. Nguyen, Numerical
reconstruction for 3D nonlinear SAR imaging via a version of the
convexification method
V. A. Khoa, M. T. N. Truong, I. Hogan, and R. Williams, Initial state
reconstruction on graphs
L. Besabe and D. Onofrei, Active control of scalar Helmholtz fields in the
presence of known impenetrable obstacles
Dinh-Liem Nguyen, Kansas State University, Manhattan, KS.
Loc Hoang Nguyen, University of North Carolina at Charlotte, NC.
Thi-Phong Nguyen, New Jersey Institute of Technology, Newark, NJ.
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