Inverse Problems and Uncertainty Quantification

Quantifying uncertainty in the solution of inverse problems is an exciting area of research in the mathematical sciences, one that raises significant challenges at the interfaces between analysis, computation, probability, and statistics. The reach in terms of applicability is enormous, with diverse problems arising in the physical, biological, and social sciences, such as weather prediction, epidemiology, and traffic flow. Loosely speaking, inverse problems confront mathematical models with data so that we can deduce the inputs needed to run the models; knowledge of these inputs can then be used to make predictions, and even to devise control strategies based on the predictions. Both the models and the data are typically uncertain, as are the resulting deductions and predictions; as a consequence, any decisions or control strategies based on the predictions will be greatly improved if the uncertainty is made quantitative.