56 citations · 510 across the 96 of their papers we have counts for
107 papers
Simultaneous Reconstructions of (x,t) -Dependent Coefficients and Initial Conditions of Parabolic Equations
Michael V. Klibanov
This is the first publication, in which an inverse problem of the simultaneous reconstruction of an unknown (x,t) - dependent coefficient and an unknown initial condition in a gene…
On an Dimensional Travel Time Tomography Problem
Michael V. Klibanov
In their seminal works Herglotz (1905) and Wiechert and Zoeppritz (1907) have solved the so-called Travel Time Tomography Problem (TTTP) in the 1-D case. However, the question abou…
Global Convergence and Uniqueness for an Inverse Problem Posed by Gelfand
Michael V. Klibanov, Jingzhi Li, Tian Niu +1
The first globally convergent numerical method is developed for a coefficient inverse problem (CIP) for the d, wave equation with the unknown potential in the most ch…
A Carleman Semi-Discrete Convexification Method Combined With Deep Learning for Electrical Impedance Tomography
Michael V. Klibanov, Kirill V. Golubnichiy, Benjamin Jiang
In this paper, a new semi-discrete version of the Carleman estimate-based convexification globally convergent numerical method is developed. It is used for the delivery of the star…
Convexification Numerical Method for Imaging of Moving Targets
Michael V. Klibanov, Jingzhi Li, Vladimir G. Romanov +1
The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and…
Toward Practical Forecasts of Public Sentiments via Convexification for Mean Field Games: Evidence from Real World COVID-19 Discussion Data
Shi Chen, Michael V. Klibanov, Kevin McGoff +3
We apply a convexification-based numerical method to forecast public sentiment dynamics using Mean Field Games (MFGs). The theoretical foundation for the convexification approach,…