Reduced Order Models for Fluid Flow With Generative Adversarial Networks

The goal of this work is to evaluate the aptness of generative adversarial networks (GANs) for use as surrogate reduced order fluid models. In contrast to previously published work, the focus is placed on analyzing the specific effect of adversarial training, by comparing GAN outcomes with those from an identical generator network trained directly on ground truth (using an L1 loss). A dataset of 10000 simulated examples of stationary flow through a 2D sudden expansion geometry containing a polygonal obstacle was created, alongside two additional datasets for testing generalization. The simulation data was interpolated to a regular image grid, and the neural networks were trained to predict the velocity field based on an image encoding the geometry.The gathered experimental data show clearly that adversarial training cannot reach the same accuracy as direct training. This was found to be true on unseen examples from the training distribution, as well as on geometries of unfamiliar type. On the other hand, GAN outcomes tend to "appear" more realistic, and exhibit a lower continuity residual. The qualitative differences were highlighted by considering bifurcation scenarios which were purposefully included in the data set. When the bifurcation parameter is at its critical value, two very different flow scenarios can occur essentially randomly. In such cases, the GAN essentially predicts just one of the possible flow outcomes, whereas the directly trained model outputs a superposition of both. This exemplifies a fundamental difference in prediction behavior.It is shown that these results can be well understood as a direct consequence of the different cost functions used during training. Furthermore, it is demonstrated that by using a sum of both types of loss functions (adversarial & L1), advantages of both models can be combined.In other results, the data show that the discriminator output cannot provide a reliable indication of the accuracy of a prediction, since no robust correlation between them was found. Also, it was observed that the discriminator appeared to dominate the adversarial game, and it was shown that improving this balance could lead to better results. Moreover, an investigation into predicting pressure alongside the velocity field was conducted. Results showed that adding an additional channel for pressure to the network architecture can achieve this goal, but is not necessary, as calculating the pressure field from the velocity output produces results of similar quality. In terms of resources, GAN training required a relative increase in computational time by approx. 50%. Additionally, GAN models were also found to take many more training steps to reach convergence. Similarly, for a fixed number of steps, results showed that directly trained models can benefit more from larger datasets. In conclusion, GAN models are likely not the right choice for reduced order modeling in scientific contexts due to their lower accuracy. However, they could hold potential for use in creating visual effects or as an added regularizer during training.Applied Mathematic