Jakob Gradl: A hybrid variational physics informed/physics encoded neural network for strictly mass-conserving joint inversion of mass and momentum balance in ice flow modelling
Physics-informed neural networks (PINNs) offer a highly flexible platform for complex data assimilation tasks that is increasingly used in glaciology. Recently, PINN-based approaches have been proposed for physically constrained interpolation of sparse ice thickness measurements based on mass conservation principles – a key development in the study of the Antarctic ice sheet that was first achieved with numerical models.
While PINNs offer computational advantages over traditional numerical approaches, they only provide approximate equation solutions which may deviate significantly from the governing equations at a local scale. Numerical ice flow models react sensitively to such physical inconsistencies, which may restrict the applicability of PINN-derived ice thickness fields as model boundary conditions.
Here, we propose a straightforward modification of the PINN framework that provides exact equation solutions. Rather than using the residual of the mass balance equation as a loss term, we use it to derive one of its component variables. This guarantees that all predicted variables are physically consistent with each other.
The momentum balance is coupled to the model in the style of a V-PINN using the weak form of the PDE as an additional loss term. While this approach doesn’t provide an exact equation solution, it is computationally advantageous as it avoids higher-order derivatives. We apply vector decomposition to the mass flux field, separating its divergent and rotational components, which stabilises the training process.
We demonstrate our method by performing joint inversions of mass-conserving ice thickness and basal friction on Denman glacier in East Antarctica.