# Generative Adversarial Reduced Order Modelling

arXiv: https://arxiv.org/abs/2305.15881 · HTML: https://mlsanity.com/paper/2305.15881/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 80 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Generative Adversarial Text to Image Synthesis](https://mlsanity.com/paper/1605.05396/) (2016)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [BEGAN: Boundary Equilibrium Generative Adversarial Networks](https://mlsanity.com/paper/1703.10717/) (2017)
- [Adversarial Uncertainty Quantification in Physics-Informed Neural Networks](https://mlsanity.com/paper/1811.04026/) (2018)
- [DIVA: Domain Invariant Variational Autoencoders](https://mlsanity.com/paper/1905.10427/) (2019)
- [A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs](https://mlsanity.com/paper/2001.04001/) (2020)
- [Taming VAEs](https://mlsanity.com/paper/1810.00597/) (2018)
- [NOMAD: Nonlinear Manifold Decoders for Operator Learning](https://mlsanity.com/paper/2206.03551/) (2022)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems](https://mlsanity.com/paper/1808.01346/) (2018)
- [Generative Adversarial Neural Operators](https://mlsanity.com/paper/2205.03017/) (2022)
- [Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows](https://mlsanity.com/paper/2109.01514/) (2021)
- [Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows](https://mlsanity.com/paper/2007.00936/) (2020)
- [A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks](https://mlsanity.com/paper/2105.13136/) (2021)
- [A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling](https://mlsanity.com/paper/2110.03442/) (2021)
- [Variational Autoencoding Neural Operators](https://mlsanity.com/paper/2302.10351/) (2023)
- [PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physics](https://mlsanity.com/paper/2106.02993/) (2021)
- [A DeepONet multi-fidelity approach for residual learning in reduced order modeling](https://mlsanity.com/paper/2302.12682/) (2023)
- [Semi Conditional Variational Auto-Encoder for Flow Reconstruction and Uncertainty Quantification from Limited Observations](https://mlsanity.com/paper/2007.09644/) (2020)
- [Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning](https://mlsanity.com/paper/2202.05460/) (2022)

## Built on by (most cited first, 7 of 7)

- [FUSE: Fast Unified Simulation and Estimation for PDEs](https://mlsanity.com/paper/2405.14558/) (2024)
- [BARNN: A Bayesian Autoregressive and Recurrent Neural Network](https://mlsanity.com/paper/2501.18665/) (2025)
- [Machine Learning Applications to Computational Plasma Physics and Reduced-Order Plasma Modeling: A Perspective](https://mlsanity.com/paper/2409.02349/) (2024)
- [Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectives](https://mlsanity.com/paper/2603.12870/) (2026)
- [PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution](https://mlsanity.com/paper/2605.03399/) (2026)
- [Patch-PODiff-ViT: Structured Latent Diffusion with Patchwise POD for Super-Resolution and Uncertainty Quantification](https://mlsanity.com/paper/2606.31290/) (2026)
- [Advances in Scientific Machine Learning for Coupled Fluid Flow and Transport](https://mlsanity.com/paper/2606.19562/) (2026)

## Abstract (arXiv)

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.