Jiapeng Liu: Solve inverse problem with physics assisted Deep Learning

Deep learning has been widely used for solving ill-posed inverse problem in the past few years. With sufficient training data, data-driven deep neural networks can serve as good approximation of mapping between input and solution. However, training set can be expensive to obtain, and consequentially, the network may not generalize well. Starting with the Deep Image Prior by Ulyanov et al, convolutional neural networks are proven to be strong prior that can solve inverse problems without training data. Recent works have explored the notion of using dataset to supervise the training process, physics priors can be added to the network architecture for even stronger constraints, and the input will be self-supervising the network. By iteratively updating the weights of the network the output generated by the network is forced to satisfy the physical model and that converges to the correct solution.