Learning parameter-dependent shear viscosity from data, with application to sea and land ice

TL;DR

This paper introduces a neural network-based framework for inferring rheological models of non-Newtonian fluids from data, ensuring physical consistency, and demonstrates its application to sea and land ice with complex, parameter-dependent behaviors.

Contribution

It presents a novel approach combining neural networks and PDE-constrained optimization to infer physically consistent rheological models from velocity and stress data.

Findings

Accurately inferred temperature-dependent Glen's law for land ice.

Successfully modeled concentration-dependent shear behavior of sea ice.

Discovered rheology models that generalize beyond training data, showing shear-thickening and thinning.

Abstract

Complex physical systems which exhibit fluid-like behavior are often modeled as non-Newtonian fluids. A crucial element of a non-Newtonian model is the rheology, which relates inner stresses with strain-rates. We propose a framework for inferring rheological models from data that represents the fluid's effective viscosity with a neural network. By writing the rheological law in terms of tensor invariants and tailoring the network's properties, the inferred model satisfies key physical and mathematical properties, such as isotropic frame-indifference and existence of a convex potential of dissipation. Within this framework, we propose two approaches to learning a fluid's rheology: 1) a standard regression that fits the rheological model to stress data and 2) a PDE-constrained optimization method that infers rheological models from velocity data. For the latter approach, we combine finite element and machine learning libraries. We demonstrate the accuracy and robustness of our method on land and sea ice rheologies which also depend on external parameters. For land ice, we infer the temperature-dependent Glen's law and, for sea ice, the concentration-dependent shear component of the viscous-plastic model. For these two models, we explore the effects of large data errors. Finally, we infer an unknown concentration-dependent model that reproduces Lagrangian ice floe simulation data. Our method discovers a rheology that generalizes well outside of the training dataset and exhibits both shear-thickening and thinning behaviors depending on the concentrations.