Globally Optimal, Data-Driven Symbolic Discovery

Tuesday, March 6, 2018 - 1:00pm - 2:00pm
Lind 305
Generalization of the behavior of a system or a phenomenon into a consistent mathematical model is instrumental for a variety of applications. Historically, models were manually derived in a first principles fashion. The first principles approach often offers the derivation of interpretable models of remarkable levels of universality while being supported by little data. Nonetheless, their derivation is time consuming and relies heavily upon domain expertise. Conversely, with the rising pervasiveness of data-driven approaches, the rapid derivation and deployment of models has become a reality. Scalability is gained through dependence upon exploitable structure (functional form). Such structures, entail non-interpretable models, demand Big Data for training, and provide limited predictive power for out-of-set instances. In this talk, we will introduce a model discovery approach that attempts to bridge between the two conducts, promoting the discovery of universal, interpretable models, using Small Data. The underlying algorithm searches for free-form symbolic models, where neither the structure nor the set of operator primitives is predetermined. The discovered models are globally optimal certified, promoting superior predictive power for unseen input. Numerical studies demonstrate the ability of the algorithm to re-discover fundamental laws of science, while references to ongoing work in the discovery of new models for, hitherto, unexplainable phenomena, will be provided.