Generative Adversarial Reduced Order Modelling
This work addresses the challenge of approximating high-fidelity models with simpler ones in computational science, representing an incremental advancement by applying GANs to a domain with limited prior research.
The authors tackled the problem of reduced order modeling for parametric differential equations by introducing GAROM, a generative adversarial network-based approach that learns solution distributions and achieves generalization with experimental evidence and convergence analysis.
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.