Design of Loss Functions for Solving Inverse Problems using Deep Learning

Solving inverse problems is a crucial task in several applications that strongly a ffect our daily lives, including multiple engineering fields, military operations, and/or energy production. There exist different methods for solving inverse problems, including gradient based methods, statistics based methods, and Deep Learning (DL) methods. In this work, we focus on the latest. Speci fically, we study the design of proper loss functions for dealing with inverse problems using DL. To do this, we introduce a simple benchmark problem with known analytical solution. Then, we propose multiple loss functions and compare their performance when applied to our benchmark example problem. In addition, we analyze how to improve the approximation of the forward function by: (a) considering a Hermite-type interpolation loss function, and (b) reducing the number of samples for the forward training in the Encoder-Decoder method.