Towards Deriving Theories from Data: Explorations of Model Inference in Geophysics

Machine learning techniques addressing classification and feature detection problems are gaining popularity in geophysics. However, there is largely untapped potential for insight generation through inference techniques that offer conclusions on what the detection of geophysical features implies. In this work, we present a first exploration on how to derive geophysical models from data by leveraging domain knowledge, symbolic computation, and genetic programming. Key ideas are discussed using case studies in volcanology and seismology. Our examples outline an algebra using geophysical genetic operators to describe models and compositions, e.g., to describe Earth deformations with different parameters, as well as the optimization process that iteratively enhances a population of models. We also address strategies of connecting hypothesized models with the empirical reality obtained through measurements such as sensor network time series and InSAR interferograms. Techniques include the derivation of invariants, i.e., measured metrics that should always be true if a model described reality; derivation of falsification test cases, i.e., examples of measurements that -if observed- would contradict a model; derivation of higher-level products such as computational interferograms of a hypothesized deformation model that can be automatically compared to empirical InSAR interferograms. Finally we present a feasibility study in Python with the gplearn framework. We acknowledge support from NASA AIST80NSSC17K0125 (PI Pankratius) and NSF ACI1442997 (PI Pankratius).