I was awarded an EPSRC Fellowship! The title is “Regularisation theory in the data driven setting”. My goal is to extend regularisation theory to the setting where there is no direct access to the forward operator at the time of solving the inverse problem and only input-output training pairs are available. Such pairs can be either collected experimentally or obtained from a computationally expensive model prior to solving the inverse problem. The latter scenario is relevant for time-sensitive applications where near real-time reconstructions are required.
Furthermore, the model free setting is the natural habitat of neural networks, and my long-term goal is to better understand their regularisation properties in the context of ill-posed inverse problems in infinite dimensions.
The fellowship is due to start in April 2021.