Inverse problems are ubiquitous in the sciences and engineering. Two categories of inverse problems pertaining to a physical system are (1) identify parameters in a model of the system from observed input-output pairs and (2) given a model of the system, determine the input to the system that caused some observed output. Applied inverse problems are challenging because a solution may (i) not exist, (ii) not be unique, or (iii) be sensitive to measurement noise contaminating the data.