A PHYSICS-INFORMED NEURAL OPERATOR FOR THE SIMULATION OF SURFACE WAVES

M. Mathias, Caio Fabricio Deberaldini Netto, Felipe Marino Moreno, Jefferson Fialho Coelho, Lucas Palmiro de Freitas, Marcel Rodrigues de Barros, Pedro C. Mello, Marcelo Dottori, F. G. Cozman, Anna Helena Reali Costa, Alberto Costa Nogueira Junior, E. Gomi, E. Tannuri
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Abstract

We develop and implement a Neural Operator (NOp) to predict the evolution of waves on the surface of water. The NOp uses a Graph Neural Network (GNN) to connect randomly sampled points on the water surface and exchange information between them to make the prediction. Our main contribution is adding physical knowledge to the implementation, which allows the model to be more general and able to be used in domains of different geometries with no retraining. Our implementation also takes advantage of the fact that the governing equations are independent of rotation and translation to make training easier. In this work, the model is trained with data from a single domain with fixed dimensions and evaluated in domains of different dimensions with little impact to performance.
用于模拟表面波的物理信息神经算子
我们开发并实施了一种神经运算器(NOp),用于预测水面波浪的演变。NOp 使用图神经网络 (GNN) 连接水面上的随机取样点,并在它们之间交换信息,从而进行预测。我们的主要贡献是在实现过程中添加了物理知识,这使得模型更具通用性,能够用于不同几何形状的领域,且无需重新训练。我们的实现还利用了控制方程与旋转和平移无关这一事实,使训练更加容易。在这项工作中,我们使用来自固定维度的单一领域的数据对模型进行了训练,并在不同维度的领域中对模型进行了评估,结果对性能影响很小。
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