A Hybrid Neural Network-Finite Element Method for the Viscous-Plastic Sea-Ice Model

We present an efficient hybrid Neural Network–Finite Element Method (NN-FEM) for the viscous–plastic (VP) sea-ice model used in climate simulations. VP solvers are costly due to the strongly nonlinear material law, with cost per degree of freedom increasing rapidly under mesh refinement. However, high resolution is needed to capture narrow deformation bands (linear kinematic features). Our approach enriches coarse-mesh FEM solutions with fine-scale corrections predicted by a locally applied neural network trained on high-resolution data. The patch-based network is small, parallelizable, and generalizes across right-hand sides and domains. Numerically, the method achieves comparable accuracy at approximately 11× lower cost and speeds Newton iterations by up to 10%.