IWR Colloquium Summer Semester 2025 Inference of Constitutive Relations From Data, With Application to Sea Ice Modeling

Sea ice is a fundamental component of the climate system and is typically treated as a continuum fluid. The most widely used sea-ice model today, proposed by Hibler in 1979, was developed from heuristic analytical arguments. Although reliable in regions of high ice concentration, it performs poorly elsewhere. In this talk, we present a general framework for inferring constitutive relations from data, and apply it to sea ice. The approach uses a characterization of isotropic constitutive laws as scalar functions of the principal invariants of the strain-rate tensor. These scalar functions are represented by neural networks trained on data generated by a Lagrangian discrete element model. By coupling PyTorch with the finite-element package Firedrake, we incorporate the governing PDE into the training process, which requires solving a PDE-constrained optimization problem for the network parameters.