# Generative Network-Based Reduced-Order Model for Prediction, Data Assimilation and Uncertainty Quantification

arXiv: https://arxiv.org/abs/2105.13859 · HTML: https://mlsanity.com/paper/2105.13859/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 86 references that are in the map.
- First posted on arXiv 28 May 2021.

## Builds on (most cited first, 20 of 20)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [GAN-based Synthetic Medical Image Augmentation for increased CNN Performance in Liver Lesion Classification](https://mlsanity.com/paper/1803.01229/) (2018)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [CycleGAN, a Master of Steganography](https://mlsanity.com/paper/1712.02950/) (2017)
- [A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems](https://mlsanity.com/paper/1908.05823/) (2019)
- [A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks](https://mlsanity.com/paper/2105.13136/) (2021)
- [An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion](https://mlsanity.com/paper/2008.10532/) (2020)
- [Data-driven modelling of nonlinear spatio-temporal fluid flows using a deep convolutional generative adversarial network](https://mlsanity.com/paper/2004.00707/) (2020)
- [Recent Developments Combining Ensemble Smoother and Deep Generative Networks for Facies History Matching](https://mlsanity.com/paper/2005.10638/) (2020)
- [Digital twins based on bidirectional LSTM and GAN for modelling the COVID-19 pandemic](https://mlsanity.com/paper/2102.02664/) (2021)
- [Data Assimilation Predictive GAN (DA-PredGAN): applied to determine the spread of COVID-19](https://mlsanity.com/paper/2105.07729/) (2021)

## Built on by (most cited first, 2 of 2)

- [Generative Adversarial Reduced Order Modelling](https://mlsanity.com/paper/2305.15881/) (2023)
- [The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantification](https://mlsanity.com/paper/2406.02204/) (2024)

## Abstract (arXiv)

We propose a new method in which a generative network (GN) integrate into a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and estimate the corresponding uncertainties associated with the states and parameters of a numerical physical simulation. The GN is trained using only unconditional simulations of the discretized PDE model. We compare the proposed method with the golden standard Markov chain Monte Carlo. We apply the proposed approaches to a spatio-temporal compartmental model in epidemiology. The results show that the proposed GN-based ROM can efficiently quantify uncertainty and accurately match the measurements and the golden standard, using only a few unconditional simulations of the full-order numerical PDE model.