Using Information Geometry to find simple models of complex processes*

Effective theories play a fundamental role in how we organize our knowledge about the world. Although reality is much more complicated than our models, we justify parsimonious representations by judiciously ignoring degrees of freedom that are irrelevant for the predictions of interest. Often, these models are related through a hierarchy of simplifying approximations that formally justify their respective domains of validity. I demonstrate how information geometry can be used to construct such effective theories for many complex systems, including systems beyond the reach of traditional methods. Embedded in the mathematical form of many model classes is a hierarchy of natural approximations. These approximations are manifest as boundaries of high-dimensional manifolds. These approximations are not black-boxes. They remain expressed in terms of the relevant combinations of mechanistic parameters and reflect the physical principles from which the complicated model was built. Furthermore, these approximations can be identified in a data-driven way for models with thousands of parameters.