10 papers
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…
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,…
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…
Forecasting Public Sentiments via Mean Field Games
Michael V. Klibanov, Kevin McGoff, Trung Truong
Motivated by the goal of forecasting public sentiments, we consider a forecasting problem in the context of the Mean Field Games theory. We develop a numerical method, which is a v…