Description:

Physics-based models of complex systems often involve a large number of unknown parameters. On the other hand the collective behavior of these systems can often be characterized by a relatively small number of phenomenological parameters. Using an information geometry approach, I argue that simple models of complex processes are often successful due to a systematic compression of microscopic details into a few effective degrees of freedom. I describe an approach to parameter reduction called the Manifold Boundary Approximation Method (MBAM) and demonstrate how it can be used to derive simple phenomenological laws from complicated mechanistic first principles. The resulting models are not black boxes, but remain expressed in terms of combinations of microscopic parameters. In this way, we explicitly connect the macroscopic and microscopic descriptions, characterize the equivalence class of systems exhibiting the same collective behavior, and identify the combination of microscopic components that function as tunable control knobs for the system behavior. I illustrate with several examples from biology and compare to other common approaches to model reduction.

Professor Mark Transtrum, Brigham Young University

Host: Michelle Driscoll

Keywords: Physics, Astronomy, Complex Systems