Deep learning enabled Lagrangian particle trajectory simulation

We introduce a deep learning method to simulate the chaotic motion of particles trapped in the recirculation zone of a buoyancy-opposed flame. The Lagrangian trajectories of particles in flame were captured using a high-speed camera and subsequently reconstructed in a 3-dimensional cylindrical space. These experimentally determined trajectories were next used to train the two most widely adopted deep generative models – the variational autoencoder (VAE) and the generative adversarial net (GAN). The performance of both models was then benchmarked according to statistical analysis performed on both the simulated trajectories and the ground truth, regarding accuracy and generalization criteria. Our results show that the GAN model produces non-repeating trajectories precisely capturing the statistical features of those determined in experiments, as revealed in their spatial-temporal scaling relationship and linear pair-correlation values; whereas the VAE model trained with the same amount of data tends to overfit, producing inferior results grappling with the trade-off between accuracy and generalization criteria. The influence of the size of training data on model performance is also evaluated. This paper concludes with a discussion on the potential utility of the deep learning enabled trajectory simulation.