CAIG: A Bayesian Inference Framework for Learning Earthquake Cycle Deformation Processes Across Scales via Novel Neural Operators

Advances in space- and ground-based monitoring have allowed scientists to improve the characterization of tectonic plate boundaries which show deformation across a vast range of spatial and temporal scales. Most dramatically, such deformation includes destructive earthquakes along faults. The exact stressors triggering earthquakes along these faults remains uncertain despite a wealth of observational data and a strong understanding of the basic physics involved. This project will employ a branch of statistical analysis, Bayesian inference, and artificial intelligence methods to move toward such a comprehensive framework of the earthquake cycle. The overall goal is to create a Bayesian framework capable of assimilating the wealth of multi-modal observational data into high resolution forward models of deformation processes to infer fault friction and rheological constitutive laws underlying transient earthquake processes in the pre/co/post seismic period. This framework will not only account for uncertainties in inferred models but will also facilitate Bayesian model selection for assessing the credibility of competing models, and Bayesian optimal experimental design for describing the information theoretic value of different observables and optimally designing future networks of instruments. This will enhance our interpretation of transient deformation in plate boundaries. This objective is intractable using current methods for Bayesian inversion, due to the high dimensionality of parameters and complexity of forward models. Surrogates in the form of neural operators—neural network approximations of maps from parameter space to observables—have the potential to make this goal tractable. In their present form, however, neural operators for infinite-dimensional parameter spaces require a prohibitive number of forward model evaluations to ensure a sufficiently accurate surrogate. The project will develop and deploy neural operators that learn the geometric structure of the physics-based input-to-observable map by incorporating low-rank Fréchet derivatives into the network architecture and training process, resulting in high accuracy surrogates with fewer training data. Complementing this research will be a training effort that builds on successful programs at UT Austin including the Jackson School of Geosciences’ Research Traineeship Experience and the Oden Institute’s Moncrief Undergraduate Summer Internship, providing training to STEM undergraduates to foster excellence in research. This award by the Division of Research, Innovation, Synergies, and Education within the Directorate for Geosciences is jointly supported by the Division of Mathematical Sciences within the Directorate for Mathematical and Physical Sciences. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.