# Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs

arXiv: https://arxiv.org/abs/1910.13444 · HTML: https://mlsanity.com/paper/1910.13444/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2019.

## Built on by (most cited first, 11 of 11)

- [PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations](https://mlsanity.com/paper/2203.11363/) (2022)
- [Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook](https://mlsanity.com/paper/2303.02063/) (2023)
- [Generative Adversarial Reduced Order Modelling](https://mlsanity.com/paper/2305.15881/) (2023)
- [Physics-Informed Machine Learning Method for Large-Scale Data Assimilation Problems](https://mlsanity.com/paper/2108.00037/) (2021)
- [Distributed Multigrid Neural Solvers on Megavoxel Domains](https://mlsanity.com/paper/2104.14538/) (2021)
- [Gaussian process regression and conditional Karhunen-Lo'eve models for data assimilation in inverse problems](https://mlsanity.com/paper/2301.11279/) (2023)
- [PCNN: A physics-constrained neural network for multiphase flows](https://mlsanity.com/paper/2109.08965/) (2021)
- [Latent Generative Modeling of Random Fields from Limited Training Data](https://mlsanity.com/paper/2505.13007/) (2025)
- [Probabilistic Matching of Real and Generated Data Statistics in Generative Adversarial Networks](https://mlsanity.com/paper/2306.10943/) (2023)
- [Conditional Korhunen-Lo'eve regression model with Basis Adaptation for high-dimensional problems: uncertainty quantification and inverse modeling](https://mlsanity.com/paper/2307.02572/) (2023)
- [ParaGAN: A Scalable Distributed Training Framework for Generative Adversarial Networks](https://mlsanity.com/paper/2411.03999/) (2024)

## Abstract (arXiv)

Uncertainty quantification for forward and inverse problems is a central challenge across physical and biomedical disciplines. We address this challenge for the problem of modeling subsurface flow at the Hanford Site by combining stochastic computational models with observational data using physics-informed GAN models. The geographic extent, spatial heterogeneity, and multiple correlation length scales of the Hanford Site require training a computationally intensive GAN model to thousands of dimensions. We develop a hierarchical scheme for exploiting domain parallelism, map discriminators and generators to multiple GPUs, and employ efficient communication schemes to ensure training stability and convergence. We developed a highly optimized implementation of this scheme that scales to 27,500 NVIDIA Volta GPUs and 4584 nodes on the Summit supercomputer with a 93.1% scaling efficiency, achieving peak and sustained half-precision rates of 1228 PF/s and 1207 PF/s.