Topological Dynamics for Metamodel Discovery with Artificial Intelligence: From Biomedical to Cosmological Technologies

Abstract

The leveraging of artificial intelligence (AI), dynamical systems have found a fertile ground for development. Machine learning is currently discovering models that provide the physical underpinnings of time series data. However, such heavily parametrized models hardly ever yield physical laws. The problem becomes daunting as we turn to the multiscale complexities of biology, biomedicine or cosmology. This book addresses this imperative as it takes the problem of AI-based model discovery to the next level where “machine intuition” is operationally defined as recognizer of rough patterns within a hierarchical representation of the time series. Thus, the book introduces topological methods that enable metamodel discovery and the proper computational tools to decode the metamodel into a relevant inferential framework that ultimately yields physical laws. Parsimonious models are traditionally cast as “sparse systems of differential equations on latent coordinates”. As this book argues, this is not the format typically adopted by AI, given the “dimensionality curse” associated with complex realities. AI demands a paradigm shift, with dynamic information translated into metamodels based on AI-interpretable patterns. These methods advance model discovery, enabling reverse engineering of time series arising from vastly complex realities that are commonplace in a broad range of fields, from biology to cosmology.