Mechanistic Modeling of Complex Processes
Physicists prefer simple models not because nature is simple, but because most of its complication is usually irrelevant. This concept is most rigorously understood using renormalization group. A microscopic, complete description of a real physical system would be unwieldy, but as we "zoom out," these countless details only influence the effective theory through a few relevant parameter combinations identifiable from macroscopic observables. For example, the BCS theory of superconductivity identifies the relevant degrees of freedom as cooper pairs--pairs of electrons that behave as though were single particle.
Many scientific fields have spent decades collecting microscopic, mechanistic information about complex processes. For example, a few minutes browsing the pathways at reactome.org reveals how daunting the scale of this information can be. What is missing, is a way of "zooming out" to understand how this information is systematically compressed into a few relevant degrees of freedom to arrive at an "effective theory".
We use information theory combined with techniques from differential geometry and topology to better understand how representations of complex systems depend on the scale at which they are probed. Our goals is to develop new theoretical tools that better leverage mechanistic insights with high-throughput, "big data" to give more predictive models of complex systems. Some of the systems we study include:
- Systems and Developmental Biology
- Power Systems
- Materials Science
- Engineered and Control Systems
The Superconducting Superheating Transition
Superconductivity has two hallmark features: zero electrical resistance and perfect diamagnetism. Diamagnetism in superconductors is known as the Meissner effect and is the mechanism behind things such as magnetic levitation. If a superconductor is placed in a large magnetic field, currents will be induced to counter act and expel the applied field. If the applied field is too large, however, the currents will exceed a critical value and the superconductor will undergo a phase transition to a normal metal. The value of the field at which this happens is known as the superheating field.
For superconductors in large magnetic fields, the transition to a normal metal can be impeded by an energy barrier resulting in a meta-stable state (similar to having 110% humidity). The initial penetration of magnetic field into the material is triggered by an instability that spontaneously breaks the symmetry of the Meissner state, mathematically similar to the Rayleigh Taylor instability. The value of the a
We use theoretical and computational tools to study the superconducting superheating transition. This work is done in collaboration with the Center for Bright Beams, an NSF funded Science and Technology Center, with the goal of finding materials with higher superheating fields. We collaborate with materials scientists from around the country using multiscale models in making materials-specific predictions that will guide the development of the next generation of particle accelerators.
Machine Learning on Acoustic Data Sets
Machine learning is a field of computer science that allows computers to automatically "learn" from data sets. It is closely related to modeling, but rather than developing models from first-principles (i.e., using physics), the computer identifies correlations in large data sets. We are using Machine Learning methods to develop predictive models from complex acoustic data sets.
In one project, our goal is to predict the ambient sound levels all over the world using only local, geospatial data. In other words, if you were given information about a location such as the local population density, distance to roads, and other similar geospatial features, could you accurately predict how loud it would be there? Which geospatial data is necessary to make an accurate prediction? The challenge is to accurately include a variety of noise sources (anthropogenic sources such as cars as well as natural sources such as flowing water and animals). Where should you collect acoustic measurements to best help the machine-learned model? These are some of the questions we explore.
In another project, our goals is to predict the evolving mood of a crowd from acoustic measurements. Imagine monitoring only the sound at a sporting event. Could you infer the dynamics of the game from this information? Now imagine monitoring a public demonstration. Could you infer the mood of a crowd and potentially prevent violent outbreaks using acoustics monitoring?