Abstract by Shane McQuarrie
Data Assimilation in the Boussinesq Approximation for Convection
Many highly developed physical models poorly approximate actual physical systems because of natural random noise. For example, convection in the earth's mantle––a fundamental process for understanding the geochemical makeup of the earth's crust and the geologic history of the earth––exhibits chaotic behavior and is therefore unpredictable. In addition, it is impossible to directly measure temperature and fluid viscosity in the mantle, and any indirect measurements are not guaranteed to be highly accurate. Over the last 50 years, mathematicians have developed a rigorous framework for reconciling noisy observations with reasonable physical models via a technique called data assimilation. We apply data assimilation to the problem of mantle convection and verify its applicability via direct numerical simulations. We also apply machine learning techniques to identify and classify relevant system features. These methods, including the simulation and analysis code, can be generalized to many other systems.