Artificial Neural Networks for Flow Field Inference

Abstract

Due to their powerful approximation capabilities, artificial neural networks have seen a wide interest in various fields. A particular application is the use of an artificial neural network to predict solutions of the governing equations for fluid flow i.e. the Navier-Stokes equations. This is done by taking the space and time variables as the inputs and the flow field variables (velocity and pressure) as outputs. Subsequently, the artificial neural network can be trained by using velocity field data on discrete points in a domain. This training is carried out by means of a scalar loss function, which is minimized by the backpropagation algorithm. By taking the gradients of the outputs with respect to the inputs, the Navier-Stokes can be formed and included in the same loss function. By including discrete velocity field data as well as the Navier-Stokes equations physics into the loss function, the trained artificial neural network could leverage its approximation capabilities to approximate the complex solutions of the flow variables. Only data on the velocity field is provided, such that the framework could be used to infer the pressure field, for which no data is given. In order to apply this approach to incompressible flows, the predicted velocity fields are strictly required to be divergence-free. To accomplish this, a divergence-free potential basis was proposed. This Data Physics Fluid Informed Neural Networks (DPFINN) framework was tested on several incompressible fluid flow test cases, for which analytical solutions were available. This work provides an extensive analysis for these test cases. The results of the test cases showed that the balance between the data and the physics loss function proved to be a delicate one, which depended on a number of different choices for the artificial neural network architectures, data and physics informing process as well as the training process. Overall, the flow fields were able to be inferred well, however simultaneous implementation of the data and the physics proved to be difficult. More complex artificial neural networks were shown to not always improve the performance. Thus, the framework results were showed to be largely dependent on the balance between the expressibility and the trainability of the framework.