Inverse Problem Solving Approach Using Deep Network Trained by GAN Simulated Data

In this paper authors deal with tasks of reliably recover a hidden multi-dimensional model parameter from indirect process observations. Such task is known as inverse problem. There are a lot of inverse problems that have practical value, for example in seismic wave propagation, low-dose tomography. To solve many of these problems in a practical style, this article proposes an approach based on the many simulations of the corresponding forward problem and using the set of simulation data as the training dataset. Most of physical processes have computer models that generate precise results. The existing simulators provide ways to predict process output by input parameters. A difficulty in solving of most inverse problems is that the solution is sensitive to variations in data, which is referred to as ill-posedness. From broad spectrum of methods to overcome ill-posedness authors use machine learning model trained on special simulated data. The paper describes the deep network model using some regularization. The key idea is to use Generative Adversarial Network (GAN) to generate correct input parameters values and support the unique existence. This network is trained by parameter examples that are real solutions of inverse problem. The small manually built dataset transforms to infinite dataset automatically by GAN. The augmented dataset feeds the simulator to get output data to train deep learning network. The network has regularization layers to support stability. The paper describes details of this model using deep augmentation to solve inverse problems on the easy example: the task of throwing a heavy ball at an angle to the horizon, taking into account the force of friction against air.