On August 20th Conor Rowan (U Colorado Boulder, Aerospace Engineering) will join us online and discuss how to best understand data-driven models at the intersection between Physics and Engineering. The talk is scheduled for 5PM CEST and will be streamed at https://unistuttgart.webex.com/unistuttgart/j.php?MTID=mff0860b2fb03c4319a2407bddeb45908.
Please note the accompanying preprint: https://arxiv.org/abs/2606.08956
An abstract of the talk follows below.
From inverse problems to neural operators: prediction, mechanism, and generalization of data-driven models
In recent years, strategies for building predictive models of physical systems from data have proliferated. From inverse problems to neural operators, all of these modeling strategies can be conceptualized as data-driven machinery to predict a system’s response over a range of inputs. Seen from this perspective, it is natural to wonder how exactly these various strategies relate to each other, and whether they can be neatly taxonomized. Drawing from the philosophical literature on scientific models, we argue that many model types have a common structure, differing only in the assumed model class of the input-output relation they define. Connecting to philosophical ideas on mechanism, and arguing that data from physical systems arises from solutions to parsimonious differential equations, we propose that only certain models are capable of mechanism discovery, and thus generalization.