  In this work, we present GAROM, a new approach for reduced order modelling
(ROM) based on generative adversarial networks (GANs). GANs have the potential
to learn data distribution and generate more realistic data. While widely
applied in many areas of deep learning, little research is done on their
application for ROM, i.e. approximating a high-fidelity model with a simpler
one. In this work, we combine the GAN and ROM framework, by introducing a
data-driven generative adversarial model able to learn solutions to parametric
differential equations. The latter is achieved by modelling the discriminator
network as an autoencoder, extracting relevant features of the input, and
applying a conditioning mechanism to the generator and discriminator networks
specifying the differential equation parameters. We show how to apply our
methodology for inference, provide experimental evidence of the model
generalisation, and perform a convergence study of the method.
