Subtle patterns and structures within observed system responses may be learned in a human-understandable form using carefully constructed deep neural networks (DNNs) that uncover solution operators governing the system. These operators can be extracted from the DNNs and examined for features that are suggestive of hidden mechanistic descriptions which then lead to testable scientific hypotheses.

The current talk briefly describes the origin and evolution of these ideas: culminating in a detailed description of the methods. We will see many interesting example applications whose source code and data are available within open, online resources that anyone can try out!