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.

翻译：本文提出GAROM，一种基于生成对抗网络（GAN）的降阶建模（ROM）新方法。GAN具有学习数据分布并生成更真实数据的潜力。尽管其已广泛应用于深度学习许多领域，但在ROM中的应用研究甚少，即用简化模型逼近高保真模型。本研究通过构建数据驱动的生成对抗模型，使之能够学习参数化微分方程的解，从而将GAN与ROM框架相结合。具体实现中，将判别器网络建模为自编码器以提取输入相关特征，同时对生成器与判别器网络施加条件机制以指定微分方程参数。我们展示了如何将该方法应用于推理，提供了模型泛化能力的实验证据，并开展了方法的收敛性研究。