A Priori Physical Information to aid Generalization Capabilities of Neural Networks for Hydraulic Modeling

A Priori Physical Information to aid Generalization Capabilities of Neural Networks for Hydraulic Modeling

Despite the significant progress achieved in computational fluid dynamics (CFD), applying CFD to large space-time domains remains a challenging task. Even when implementing several simplifications, simulating environmental fluid dynamics can require a high computational burden. Recently, Physics-Informed Neural Networks (PINNs) have been applied to a wide range of problems and have proven to be more practical than classical techniques. PINNs have the potential to solve complex partial differential equations (PDEs), which are significant for physics and engineering. Physics-Informed Machine Learning (PI-ML) techniques involve introducing physically-based constraints into existing ML models. These constraints typically require compliance with conservation equations. By doing so, it is possible to reduce the machine's learning time, increase its generalization capabilities, and obtain physically-based results.

The goal of this research project is to integrate High Performance Computing (HPC) in CFD, particularly in hydraulics, with Machine Learning (ML) strategies to create a fully integrated computational platform. This technique can be applied to a typical problem of environmental fluid dynamics, such as the perimeter of flood areas. After generating sufficient results using standard techniques, the machine will be trained using these results and some physical constraints to interpolate them as the flood wave or geometry varies.

The methods used in this research project involve adapting ML algorithms to solve various engineering problems in the field of environmental hydraulics. To obtain physically-based solutions, the loss function of the ML model will be modified. This will help the model converge to physically-realistic solutions.