Predictive, causal modeling in the era of Big Data and High-Performance Computing

We are continually gathering larger amounts and kinds of data about real systems, and have increasingly higher expectations of detail and fidelity in the models we build of those systems. As we try to incorporate more detail and broader domains into our predictive mathematical models, we become less able to intuit their working principles. While simulation of large-scale models can demonstrate sufficiency of the model to capture a phenomenon, it generally does not lead to an analytical understanding of the minimally sufficient causes of that phenomenon, which may belong to a subset of the model’s many components. Understanding minimal descriptions of behavior is valuable for making principled, predictable, and efficient changes to the behavior, for instance to design a new treatment for a disease.

On the other hand, highly simplified, abstract models are popular ways to represent intuition about mechanisms. These are generally not derived or inferred using systematic principles directly from a detailed model, and so we often remain unsure whether we have found the correct low-dimensional representation of a mechanism. If we have, how do we know how to relate adjustments to the reduced model to corresponding changes in the detailed model without an explicit mapping between the representations?

The qualitative theory of dynamical systems and the methods of asymptotic analysis contain many useful tools for understanding models at multiple scales and levels of representation.  In this talk, I describe how I have interpreted and augmented these methods into practical algorithms that allow their partial automation in software. As a result, high-dimensional dynamics that were previously inaccessible to pen-and-paper analysis can now be understood and visualized through computer-assisted systematic reduction.

This talk will show examples of these methods applied to several biological problems, including the inference of mechanism for plateau potentials in a detailed cardiac myocyte model.