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

Ruibiao Zhu

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.

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

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.
Paper Structure (33 sections, 1 theorem, 39 equations, 15 figures, 7 tables, 2 algorithms)

This paper contains 33 sections, 1 theorem, 39 equations, 15 figures, 7 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Methods
  3. Results
  4. Conclusions
  5. Supplementary information: kalman filter (KF)
  6. Ensemble kalman filter (EnKF)
  7. Prediction step
  8. Update step
  9. Ensemble transform kalman filter (ETKF)
  10. Prediction step
  11. Update step
  12. Results for CN with DA in 10 floes and 30 floes situation
  13. Supplementary information: sender and receiver relation matrices
  14. Definition of sender and receiver relation matrices
  15. Indexing of nodes and edges
  16. ...and 18 more sections

Key Result

Lemma 1

Given relation matrices $R_s$ and $R_r$ for a graph where a relation between two nodes is represented as two directional edges, there exists a column permutation of one of the matrices to represent the other one. The permutation would be column $i$ and column $j$ when two directional edges are index

Figures (15)

  • 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 3: The illustration of experiment settings. The boundaries are shown as black walls, and the floes are represented as circles.
  • 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.
  • 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.
  • ...and 10 more figures

Theorems & Definitions (2)

  • Lemma 1
  • Remark 1