The Department of Mathematics, The Chinese University of Hong Kong (CUHK) invites the application for one PhD under the supervision of Prof. Bangti Jin. The position is funded by the international joint supervision of PhD students scheme of CUHK, with Prof. Simon Arridge at University College London as the co-supervisor. The studentship is for three years for an appointee with research MSc degree, and four years for an appointee with the bachelor degree. The goal of the project is to investigate the use of deep neural networks for solving inverse problems associated with partial differential equations, with a focus on developing efficient numerical algorithms and / or providing theoretical guarantees. The specific inverse problems of interest include electrical impedance tomography, current density impedance imaging and conductivity imaging from partial interior data. The topics deal with the development and application of neural networks and their integration to inverse problems, and the main tasks include

1) conduct numerical experiments on model inverse problems

2) conduct preliminary theoretical analysis of the algorithm, e.g., generalization error analysis

3) perform comparative study with traditional methods

The deadline for the application is August 31, 2023, and the application and questions on the position should be directed to Bangti Jin (b.jin@cuhk.edu.hk)