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：本文提出了一种基于生成对抗网络的新型降阶建模方法——GAROM。生成对抗网络具备学习数据分布并生成更逼真数据的潜力。尽管该技术在深度学习诸多领域已获广泛应用，但其在降阶建模（即用简化模型逼近高保真模型）中的应用研究尚显不足。本研究通过构建数据驱动的生成对抗模型，将GAN与ROM框架相结合，实现了对参数微分方程解的学习。具体而言，我们将判别器网络建模为自编码器以提取输入数据的相关特征，并在生成器与判别器网络中引入指定微分方程参数的条件机制。本文阐述了该方法在推理任务中的应用路径，通过实验验证了模型的泛化能力，并对方法进行了收敛性分析。