Graph neural network for colliding particles with an application to sea ice floe modeling

Accurate modeling of sea ice concentration (SIC) evolution is essential for polar climate assessment and short?range sea ice prediction. Numerical and data-driven approaches constitute major foundations for SIC modeling, but the former often require complex parameterizations and substantial compu?tation, whereas the latter rarely encode physical dependencies explicitly. This study presents the Physics-Informed Hybrid Ice Model (PIHIM), a differentiable data-driven hybrid ice model for daily SIC evolution that organizes its network structure according to the physical dependencies encoded in the sea ice continuity equation and explicitly accounts for dynamical transport, ther?modynamically driven areal growth and loss, and unresolved local processes. PIHIM preserves the representation capacity of deep learning while providing a process-decomposed formulation of ice displacement, freeze-melt areal change, and local error closure. Two evaluation settings are adopted: reanalysis-forced simulation examines SIC evolution stability under reanalysis forcing, and forecast-forced prediction assesses short-range performance un?der forecast-forced conditions, with reanalysis and observational SIC serving as verification references. Results indicate enhanced ice-edge preservation and error-growth control in reanalysis?forced simulation, while PIHIM retains measurable short-range prediction skill under forecast-forced conditions. Our code will be made publicly available after the paper is accepted.

Ocean dynamics are inherently chaotic, yet existing machine learning ocean models produce only deterministic forecasts. We introduce Njord, a probabilistic data-driven model for ocean forecasting, applicable to both global and regional domains. Njord combines a deep latent variable framework with a graph neural network architecture, enabling sampling each forecast step in a single forward pass. We apply Njord globally at 0.25° resolution and regionally to the Baltic Sea at 2 km resolution. To scale to these large ocean grids we introduce K-means cluster meshes that adapt to irregular sea surface geometry. Experiments demonstrate strong performance on both domains compared to deterministic machine learning baselines, while also providing uncertainty estimates from the sampled ensemble forecasts. On the global OceanBench benchmark, Njord achieves the lowest errors on average across upper-ocean variables when evaluated against real-world observations, with the largest improvements in surface temperature prediction.

Accurate modeling of the daily evolution of sea ice concentration (SIC) is central to improving the credibility and operational forecasting capability of deep learning-based sea ice prediction. However, existing deep learning methods often couple the underlying sea ice evolution relationships and data errors within high-dimensional nonlinear mappings, making it difficult to construct a stable and verifiable evolution core and apply it reliably to practical forecasting. To address this issue, this study proposes a reanalysis-forecast dual-domain decoupled framework for learning sea ice evolution operators. The framework builds upon a lightweight physical baseline to generate daily evolution trajectories, employs a temporally constrained joint multi-lead compensation network to com?pensate for unresolved processes, and introduces an ice-mass?aware transport mechanism to suppress numerical dissipation. In the forecasting stage, the parameters of the base evolution core are fixed, while a lightweight variable-semantic adaptation mechanism calibrates inter-domain distributions and evolution responses, thereby separating forecast-domain errors from base evolution errors. Experiments show that the constructed base evolution core can accurately and stably simulate daily sea ice evolution at both short-term and annual scales under reanal?ysis forcing, and can be effectively transferred to the forecast domain through lightweight adaptation, achieving stable prac?tical forecasting capability while preserving the base evolution structure. The source code will be made publicly available at https://github.com/zhangmaqun65535/SNM upon acceptance of this manuscript.