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

Ruibiao Zhu

cs.LGFeb 18, 2026

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

Authors: Ruibiao Zhu

Organizations: College of Systems and Society, The Australian National University, ACT, 2600, Australia.

Abstract

This paper introduces a novel approach to sea ice modeling using Graph Neural Networks (GNNs), utilizing the natural graph structure of sea ice, where nodes represent individual ice pieces, and edges model the physical interactions, including collisions. This concept is developed within a one-dimensional framework as a foundational step. Traditional numerical methods, while effective, are computationally intensive and less scalable. By utilizing GNNs, the proposed model, termed the Collision-captured Network (CN), integrates data assimilation (DA) techniques to effectively learn and predict sea ice dynamics under various conditions. The approach was validated using synthetic data, both with and without observed data points, and it was found that the model accelerates the simulation of trajectories without compromising accuracy. This advancement offers a more efficient tool for forecasting in marginal ice zones (MIZ) and highlights the potential of combining machine learning with data assimilation for more effective and efficient modeling.

Figures & tables

Figure 1: The illustration of CN predictions with only initial states as inputs. In the visualization, different floes are distinguished by representing each with a uniquely colored circle. The predicted state at time $t$ is denoted with a tilde ( $\tilde{X}_{t}$ ) over the head, while the ground truth state at time $t$ is represented without the tilde ( $X_{t}$ ). The white box represents the input of the model, and blue shaded box stand for the output of the model, and the arrow shows the data flows. The proposed model CN recursively utilizes information from the previous two-time steps to forecast the state at the subsequent time step, predicting the states for all times, except for the initial two-time steps which serve as ground truth inputs.

Figure 2: The illustration of computing the overlap distance $\delta_{n}^{ij}$ when the two floes contact with each other.

Figure 4: The illustration of graph construction for GNN. The boundaries are shown as black walls, and $e$ represents the edge, and $x$ stands for the node.

Model	Simulation RMSE	one-step position RMSE	one-step velocity RMSE	PCC
GNS Sanchez-Gonzalez et al. (2020)	8.897476	0.001089	1.536386	-0.243754
Interaction Network Battaglia et al. (2016)	11.490381	0.000038	0.373804	0.567590
CN with one step	4.482929	0.000010	0.070539	0.712879
CN with Mish	2.334024	0.000006	0.028410	0.934317
CN with ReLU	3.048421	0.000015	0.117186	0.894427
CN with SiLU	2.452933	0.000009	0.065283	0.927664

Table 1: Model performance comparison

Simulation time range	PCC	Simulation RMSE
10000	0.934	2.334
20000	0.871	4.256
30000	0.791	7.230
40000	0.576	11.055

Table 2: Model generalization comparison

Panel of Figure 5 — Figure 5: The PCC plots for CN in inference. The x-axis is the index of floes, and the y-axis is the PCC value.

Panel of Figure 6 — Figure 6: The PCC plots for CN with ENKF and ETKF in inference. The x-axis stands for different noise levels for model and observation, and the y-axis is the PCC value. Suffix stands for the observation frequency. For example, ENKF_100 means the model couples the ENKF, and observes the half states with a specific noise level every 100-time steps.

Panel of Figure 7 — Figure 7: The RMSE plots for CN with ENKF and ETKF in inference. The x-axis stands for different noise levels for model and observation, and the y-axis is the RMSE value. Suffix stands for the observation frequency. For example, ENKF_100 means the model couples the ENKF, and observes the half states with a specific noise level every 100-time steps.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Model noise	Observation noise	ENKF 100	ETKF 100	ENKF 500	ETKF 500
		PCC
0.1	0.1	0.99348	0.99313	0.90178	0.89945
0.1	1.0	0.99220	0.99207	0.89765	0.89774
0.1	2.0	0.99042	0.99073	0.89908	0.89312
1.0	0.1	0.99040	0.99057	0.88816	0.88732
1.0	1.0	0.99005	0.99017	0.89026	0.89120

Appendix

Table 3: PCC for ENKF and ETKF in 10 floes with different noise levels

Model noise	Observation noise	ENKF 100	ETKF 100	ENKF 500	ETKF 500
		RMSE
0.1	0.1	0.87184	0.89075	3.47952	3.51363
0.1	1.0	0.98809	0.99665	3.56790	3.56005
0.1	2.0	1.10862	1.09638	3.57505	3.64760
1.0	0.1	1.08139	1.07064	3.73382	3.83360
1.0	1.0	1.09488	1.08325	3.70420	3.68827

Appendix

Table 4: RMSE for ENKF and ETKF in 10 floes with different noise levels

Model noise	Observation noise	ENKF 100	ETKF 100	ENKF 500	ETKF 500
		PCC
0.1	0.1	0.99348	0.99135	0.89735	0.89360
0.1	1.0	0.98932	0.98951	0.89713	0.89262
0.1	2.0	0.98749	0.98713	0.89187	0.89227
1.0	0.1	0.98755	0.98778	0.87743	0.88166
1.0	1.0	0.98700	0.98739	0.87368	0.88840

Appendix

Table 5: PCC for ENKF and ETKF in 30 floes with different noise levels

Model noise	Observation noise	ENKF 100	ETKF 100	ENKF 500	ETKF 500
		RMSE
0.1	0.1	0.84700	0.84920	3.07565	3.11070
0.1	1.0	0.97852	0.97021	3.07969	3.14298
0.1	2.0	1.08828	1.10031	3.16782	3.15995
1.0	0.1	1.04012	1.03504	3.37514	3.36270
1.0	1.0	1.07427	1.06559	3.44587	3.25165

Appendix

Table 6: RMSE for ENKF and ETKF in 30 floes with different noise levels

Panel of Figure 8 — Figure 8: Illustration of constructing graphs (Circle represents node, and arrow represents edge)

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