Ngoc Hien Nguyen

• Simulating complex physical systems involves solving nonlinear partial differential equations (PDEs), which can be very expensive. Generative Adversarial Networks (GAN) has recently been used to generate solutions to PDEs-governed complex systems without having to numerically solve them. However, concerns are raised that the standard GAN system cannot capture some important physical and statistical properties of a complex PDE-governed system, along side with other concerns for difficult and unstable training, the noisy appearance of generated samples and lack of robust assessment methods of the sample quality apart from visual examination. In this thesis, a standard GAN system is trained on a data set of Heat transfer images. We show that the generated data set can capture the true distribution of training data with respect to both visual and statistical properties, specifically the vertical statistical profile. Furthermore, we construct a GAN model which can be conditioned using variance-induced class label. We show that the variance threshold t = 0. 01 constructs a good conditional class label, such that the generated images achieve 96% accuracy rate in complying with the given conditions.