Prediction of Sea Ice Velocity and Concentration in the Arctic Ocean using Physics-informed Neural Network

TL;DR

This work addresses the challenge of predicting Arctic sea ice dynamics under a non-stationary climate by marrying physics with data-driven learning. It introduces a physics-informed neural network (PINN) built on the Hierarchical information-sharing U-net (HIS-Unet) that jointly predicts sea ice velocity $SIV$ and sea ice concentration $SIC$, guided by physics losses and a sigmoid constraint to enforce physical bounds. The approach yields consistent improvements over a fully data-driven baseline, particularly when training data are scarce, with notable gains in central Arctic regions and for SIC during melting/freezing periods. These results demonstrate enhanced generalizability and physical plausibility, suggesting a robust path forward for climate-adaptive sea ice forecasting and potential extensions to recurrent architectures for multi-day forecasts.

Abstract

As an increasing amount of remote sensing data becomes available in the Arctic Ocean, data-driven machine learning (ML) techniques are becoming widely used to predict sea ice velocity (SIV) and sea ice concentration (SIC). However, fully data-driven ML models have limitations in generalizability and physical consistency due to their excessive reliance on the quantity and quality of training data. In particular, as Arctic sea ice entered a new phase with thinner ice and accelerated melting, there is a possibility that an ML model trained with historical sea ice data cannot fully represent the dynamically changing sea ice conditions in the future. In this study, we develop physics-informed neural network (PINN) strategies to integrate physical knowledge of sea ice into the ML model. Based on the Hierarchical Information-sharing U-net (HIS-Unet) architecture, we incorporate the physics loss function and the activation function to produce physically plausible SIV and SIC outputs. Our PINN model outperforms the fully data-driven model in the daily predictions of SIV and SIC, even when trained with a small number of samples. The PINN approach particularly improves SIC predictions in melting and early freezing seasons and near fast-moving ice regions.

Figures (7)

• Figure 1: (a) Architecture of Hierarchical information-sharing U-net (HIS-Unet); (b) Weighting attention module (WAM) in HIS-Unet; (c) Channel attention module and (d) Spatial attention module in a WAM koo2023_hisunet.
• Figure 2: (a) The reduction of SIV RMSE by PINNs with different training sample sizes (20, 50, and 100 %) and combinations of $\lambda_{sat}$ and $\lambda_{therm}$ (0, 0.2, 1.0, and 5.0), relative to the SIV RMSE of the No-Phy model. (b) The reduction of SIC RMSE by PINNs with different training sample sizes and combinations of $\lambda_{sat}$ and $\lambda_{therm}$, relative to the SIC RMSE of the No-Phy model. Cross markers indicate statistically significant reduction.
• Figure 3: Monthly SIV RMSE of No-Phy model and PINN ($\lambda_{sat}=0.2$ and $\lambda_{therm}=0.2$) for seven test years (2016-2022). On the top panel, the solid lines indicate monthly SIV RMSEs of PINN models, and the dashed lines indicate No-Phy models. The bottom panel shows the differences between each PINN model and the No-Phy model. Statistically significant decreases in RMSE by PINN are highlighted as circles in the bottom panel. Statistical significance of each month is determined by conducting a t-test on all daily RMSE results from PINN and No-Phy. The shaded areas in the bottom panels show the 25-75 % quantile of RMSE difference.
• Figure 4: Monthly SIC RMSE of No-Phy model and PINN ($\lambda_{sat}=0.2$ and $\lambda_{therm}=0.2$) for seven test years (2016-2022). On the top panel, the solid lines indicate monthly SIC RMSEs of PINN models, and the dashed lines indicate No-Phy models. The bottom panel shows the differences between each PINN model and the No-Phy model. Statistically significant decreases in RMSE by PINN are highlighted as circles in the bottom panel. Statistical significance of each month is determined by conducting a t-test on all daily RMSE results from PINN and No-Phy. The shaded areas in the bottom panels show the 25-75 % quantile of RMSE difference.
• Figure 5: The SIV RMSE map of the No-Phy model for (a) 20 % training samples, (b) 50 % training samples, and (c) 100 % training samples. The SIV RMSE map of the PINN model ($\lambda_{sat}=0.2$ and $\lambda_{therm}=0.2$) for (d) 20 % training samples, (e) 50 % training samples, and (f) 100 % training samples. The relative SIV RMSE difference map between PINN and No-Phy model for (g) 20 % training samples, (h) 50 % training samples, and (i) 100 % training samples. On the bottom panels of the RMSE differences, the reddish color indicates the improvement in SIV RMSE by PINN over the No-Phy model (i.e., reduction in RMSE).