Mathematics

Partial differential equations (PDEs) are invaluable tools for modeling complex physical phenomena. However, only a limited number of PDEs can be solved analytically, leaving the majority of them requiring computationally expensive numerical approximations. To address this challenge, reduced order models (ROMs) have emerged as a promising field in computational sciences, offering efficient computational tools for real-time simulations. With the advent of abundant data resources, data-driven ROMs have gained significant attention within the scientific community due to their ability to model systems using only a small amount of data. In recent years, deep learning discriminative-based techniques have played a pivotal role in advancing efficient ROM methods with exceptional generalization capabilities and reduced computational costs. In this talk, we will discuss the latest advancements achieved through the utilization of deep learning generative-based techniques for ROM. In particular, we illustrate how deep latent variable models can be used for ROM, focusing on GAROM, a recently proposed approach based on generative adversarial learning.