Session: 08-09-01 Neural Network for Waves & Cylinders, Symposium Summary

Paper Number: 104950

104950 - A Physics-Informed Neural Operator for the Simulation of Surface Waves 

Fluid simulation is a notoriously complex and expensive task; it is, however, an essential step in the design and validation of offshore structures. In this work, we develop a Physics-Informed Machine Learning (PIML) model that can predict the temporal evolution of waves on the surface of water. The concept behind PIML is to combine data-driven machine learning models to physics-driven numerical simulations to benefit from the best characteristics of each methodology. We develop a Neural Operator (NOp) that maps a snapshot of the water surface at a given instant to a prediction of its state in the future.
We apply this model to the Hydrodynamic Calibrator water test tank at the Numerical Offshore Tank facilities a university; nonetheless, the model is intended to be general and could be easily adapted to other scenarios. The model is resolution-independent and rotation- and translation-agnostic; which means that, once trained, it can be used for simulations of any grid resolution and even in tanks of different shapes.
NOp works by distributing randomly sampled points along the domain and connecting them via a Graph Neural Network (GNN). Initially, each node of the graph represents the current state of the tank at its location, in an encoded state. The edges connecting neighboring nodes contain encoded information on the physical distance between them. The GNN model works by exchanging messages between the neighboring nodes; each exchange depends on the information contained in the edge, and updates the values contained in the nodes. This message passing cycle is repeated a number of times; after which, the information in each node is decoded to the future state of the water surface. Each encoding and decoding step is performed by a Multi-Layer Perceptron (MLP).
One of the main contributions of this work is that NOp was designed in a way to make it agnostic to rotation and translation, which dramatically increases its flexibility and eases its training when compared to a model that is dependent on its absolute position on the body of water. This was possible due to a rearranging of the boundary conditions at the sides of the tank. All boundaries in this case are considered fixed walls, which, in terms of wave propagation, act virtually the same as a symmetry condition. In our implementation, we do not implement the boundary conditions directly, instead, graph nodes that are close to the walls can connect to both real nodes, inside the domain, and to phantom nodes, which lie outside of the domain, but perfectly mirror the state inside of it.
We believe this technique can be extended to more complex problems, such as the simulation of water currents in domains with more complicated geometries. Furthermore, the encoding models used could be possibly swapped to ones that are aware of temporal evolution, allowing us to predict not only a snapshot but a full-time series.

Presenting Author: Marlon Sproesser Mathias Universidade de São Paulo

Presenting Author Biography: Postdoctoral researcher at the Center for Artificial Intelligence, at University of São Paulo (C4AI-USP), in the project "Physics-Informed Machine Learning applied to the prediction of ocean variables". Master and Doctor in Mechanical Engineering from the São Carlos School of Engineering, USP (EESC-USP), having worked with numerical simulation of fluids, in particular the hydrodynamic instability that leads to the transition to turbulence. Aeronautical Engineer also from EESC-USP.

Authors:

Marlon Sproesser Mathias Universidade de São Paulo
Caio Fabricio Deberaldini Netto University of São Paulo
Felipe Marino Moreno University of São Paulo
Jefferson Fialho Coelho University of São Paulo
Lucas Palmiro De Freitas University of São Paulo
Marcel Rodrigues De Barros University of São Paulo
Pedro Cardozo De Mello University of São Paulo
Marcelo Dottori University of São Paulo
Fábio Gagliardi Cozman University of São Paulo
Anna Helena Reali Costa University of São Paulo
Alberto Costa Nogueira Junior IBM Research
Edson Satoshi Gomi University of São Paulo
Eduardo Aoun Tannuri University of São Paulo