Deep Learning for Inverse Problems in Engineering and Science

Abstract

In a famous Socratic dialogue by Plato, Meno postulates that the epistemic pursuit of knowledge demands a target, without which one cannot determine the object of inquiry or even recognize it upon discovery. The paradox resonates with the enigmatic, blackbox nature of deep learning; the abundance of data in fields such as computer vision and natural language processing and increasingly massive computational power has perhaps impeded a thorough understanding of these machines. We may fall victim to Meno's Paradox, namely the inability to reap the full benefits of deep learning's remarkable capabilities for engineering and science at large. To date, deep learning applications are fairly unexplored in data-scarce scientific and engineering fields with rich mathematical grounding such as the theory of optimization for solving inverse problems, or those in which interpretability matters. In such domains, the goal often goes beyond data fitting, and extends to advancing scientific discoveries. In this context, this dissertation imposes an inductive bias on deep neural networks to discover human-understandable patterns for science and improve the efficiency and performance in unsupervised or data-scarce inverse problems in engineering.