Computational Mathematics and Scientific Computing Seminar

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Sea ice is a fundamental component of the climate system that is generally treated as a continuum fluid in Earth system models. A key component in continuum models for sea ice is its rheology, which establishes a relationship between strain-rate, the Cauchy stress tensor, and other variables such as sea ice concentration and thickness. Traditionally, rheological models for complex systems such as sea ice have been derived by means of phenomenological or highly simplified analytical arguments, compromising their accuracy. Discrete element methods (DEMs) offer an alternative to continuum models by resolving the behavior of individual ice floes, including collisions, frictional contact, fracture, and ridging. However, DEMs are generally too costly for large-scale simulations. In this talk, I will present a framework for inferring rheological behavior from velocity data generated with a DEM. We characterize isotropic constitutive laws in terms of scalar functions of the principal invariants of the strain-rate tensor. These functions are parameterized by neural networks trained on DEM data. By combining machine learning and finite element methods, we incorporate the governing partial differential equation (PDE) into the training, leading to a PDE-constrained optimization problem for the network parameters. We find that, over a wide range of ice concentrations, the velocity fields observed in a complex sea ice DEM can be captured by a nonlinear rheology. We also show that the learned rheology generalizes to different forcing scenarios, time-dependent problems, and settings in which compressibility is not a dominant factor.