A unified framework for forward and inverse modeling of ice sheet flow
using physics-informed neural networks
Abstract
Predicting the future contribution of the ice sheets to sea level rise
over the next decades presents several challenges due to a poor
understanding of critical boundary conditions, such as basal sliding.
Traditional numerical models often rely on data assimilation methods to
infer spatially variable friction coefficients by solving an inverse
problem, given an empirical friction law. However, these approaches are
not versatile, as they sometimes demand extensive code development
efforts when integrating new physics into the model. Furthermore, this
approach makes it difficult to handle sparse data effectively. To tackle
these challenges, we propose a novel approach utilizing Physics-Informed
Neural Networks (PINNs) to seamlessly integrate observational data and
governing equations of ice flow into a unified loss function,
facilitating the solution of both forward and inverse problems within
the same framework. We illustrate the versatility of this approach by
applying the framework to two-dimensional problems on the Helheim
Glacier in southeast Greenland. By systematically concealing one
variable (e.g. ice speed, ice thickness, etc.), we demonstrate the
ability of PINNs to accurately reconstruct hidden information.
Furthermore, we extend this application to address a challenging mixed
inversion problem. We show how PINNs are capable of inferring the basal
friction coefficient while simultaneously filling gaps in the sparsely
observed ice thickness. This unified framework offers a promising avenue
to enhance the predictive capabilities of ice sheet models, reducing
uncertainties, and advancing our understanding of poorly constrained
physical processes.