CDI-Type I: Distilling Freeform Natural Laws from Experimental Data

Cornell University, Ithaca NY

Investigators

Abstract

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The objective of this research is to develop general-purpose algorithms for automatically identifying principles underlying observed phenomena, in fields ranging from physics to biology. For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power in scientific inquiry, finding natural laws and their corresponding equations has resisted automation. The approach is based on symbolic regression methods that can search for equations that describe invariant quantities in time-series data. Seeking invariants usually leads to deeper insights than prediction alone: For example, seeking invariant quantities in a pendulum motion leads to discovery of the conservation of energy. With respect to intellectual merit, the research seeks new algorithms to automatically search for implicit models that are conserved over the data and, simultaneously, search for new experiments that cause maximum disagreement between competing model predictions. A key challenge to finding analytic relationships automatically is defining algorithmically what makes a correlation in observed data significant and non-trivial. The ultimate milestone will be for the proposed method to identify yet-unknown laws in new systems such as biology, where natural laws and conservations are difficult to find. With respect to broader impact, the research addresses the need for methods to automatically and dynamically synthesize both the structure and parameters of models of nonlinear systems in many fields. The ability to actively infer models from behavior can be applied to create models of both engineered and natural systems from robotics to biological networks to human behavior.