The operational limits of open-ocean aquaculture cages are governed by the large, wave- and current-driven deformations of their flexible structures. To study this problem, we generate simu- lation data with a finite element analysis model driven by a Morison-type hydrodynamic loading, distributed along net elements. The dataset encompasses a wide range of sea states and structural parameters, storing nodal displacements relative to the undeformed configuration at each time step. To accelerate the prediction, we introduce our recently developed MeshODENet, which combines Neural Ordinary Differential Equations (ODE) and a Graph Neural Network model. Coupled with an adaptive ODE solver, our MeshODENet generates stable, and accurate multi-step rollouts to predict the large deformations of aquaculture nets. This physics-informed machine learning method enables rapid simulation of aquaculture system dynamics in complex ocean conditions.
We simulate the dynamics of the aquaculture net using a truss-based finite element analysis (FEA) model. Hydro- dynamic forcing follows a modified Morison force equation
with drag and inertia terms applied along net members using the relative fluid–structure kinematics. Parameter sweeps varied wave spectra, current profiles, structural stiffness, and mass. We record the dynamics of nodal po- sitions and velocities over time, as well as the element connectivity. However, FEA-based models are computa- tionally expensive and cannot predict large net deforma- tions in real-time.
To tackle this challenge, we introduce the MeshODENet model, which combines Neural Ordinary Differential
Equations and a Graph Neural Network model. The model uses a multi-layer perceptron message-passing block to parameterize the time derivative of nodal states. The system’s state is advanced by integrating this learned vector field with an adaptive ODE solver. We use the MeshODENet to predict the future dynamics given each node’s previous states, which include the positions and velocities. The model was trained by minimizing rollout error on sequences from 1000 simulated cases and evalu- ated on disjoint sea states to assess generalization.
Across unseen conditions, the MeshODENet reproduces structural dynamics with low error and minimal drift over long horizons. Figure 1 and 2 compare ground truth (FEA) and MeshODENet predictions, showing that the
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MeshODENet model captures global deformation patterns and localized responses near high-curvature regions. The MeshODENet model also achieves dynamics predic- tions orders of magnitude faster than traditional FEA. This work lays the foundation for a digital-twin platform for aquaculture infrastructure, which will enable precision aquaculture through real-time condition monitoring.