Investigation of Applying Physics Informed Neural Networks (PINN) and Variants on 2D Aerodynamics Problems

Abstract

Investigation of applying physics informed neural networks on the test case involving flow past Converging-Diverging (CD) Nozzle has been investigated. Both Artificial Neural Network (ANN) and Physics Informed Neural Network (PINN) are used to do the training and prediction. Results show that Artificial Neural Network (ANN) by itself is already able to give relatively good prediction. With the addition of PINN, the error reduces even more, although by only a relatively small amount. This is perhaps due to the already good prediction. The effects of batch size, training iteration and number of epochs on the prediction accuracy have already been tested. It is found that increasing batch size improves the prediction. On the other hand, increasing the training iteration may give poorer prediction due to overfitting. Lastly, in general, increasing epochs reduces the error. More investigations should be done in the future to further reduce the error while at the same time using less training data. More complicated cases with time varying results should also be included. Extrapolation of the results using PINN can also be tested.

Physics-informed neural networks for modeling astrophysical shocks

“…In recent years, PINNs have been successfully used for tackling a range of fluid dynamics forward and inverse problems amongst which, there has also been a handful of studies modeling shock waves [20][21][22]. This is the first paper that uses PINNs to model the heliospheric termination shock from the base of the solar corona to the edge of the heliosphere including the gravitational force and a heating proxy.…”

“…Physics-informed neural networks (PINNs) are a special category of deep learning models that combine the power of partial differential equations (PDEs) and neural networks to solve a wide range of problems ranging from cases with no data available to data-driven approaches [17][18][19][20][21][22]. PINNs leverage the power of automatic differentiation-a property of deep learning models [see e.g.…”

“…Over the last decade, a number of papers have been published on the applicability of PINNs forward problems on fluid dynamics use-cases [17,18,[20][21][22]32]. While PINNs have been successful in the forward modeling of simpler physical scenarios, they still suffer from (a) low accuracy even with many training points, (b) local minima in cases of non-convex solution spaces and (b) lack of general applicability and high costs as they require extensive hyper-parameter tuning especially for complex physical setups such as compressible fluids and discontinuities [33,34, see e.g.…”

“…In a number of recent works PINNs have been used for modeling simpler and classic shock wave problems [17,[20][21][22]. While there have been machine learning studies on interstellar shock prediction or Coronal Mass Ejection transit times [40,41], there have not been any PINNs studies investigating astrophysical shocks in the presence of a gravitational field.…”