# The efficacy and generalizability of conditional GANs for posterior inference in physics-based inverse problems

arXiv: https://arxiv.org/abs/2202.07773 · HTML: https://mlsanity.com/paper/2202.07773/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 15 Feb 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [A Learned Representation For Artistic Style](https://mlsanity.com/paper/1610.07629/) (2016)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations](https://mlsanity.com/paper/1811.02033/) (2018)
- [Augmented CycleGAN: Learning Many-to-Many Mappings from Unpaired Data](https://mlsanity.com/paper/1802.10151/) (2018)
- [Deep Bayesian Inversion](https://mlsanity.com/paper/1811.05910/) (2018)
- [Composing Normalizing Flows for Inverse Problems](https://mlsanity.com/paper/2002.11743/) (2020)
- [Solving Bayesian Inverse Problems via Variational Autoencoders](https://mlsanity.com/paper/1912.04212/) (2019)
- [A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks](https://mlsanity.com/paper/2105.13136/) (2021)
- [Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priors](https://mlsanity.com/paper/2107.02926/) (2021)
- [Parameterizing uncertainty by deep invertible networks, an application to reservoir characterization](https://mlsanity.com/paper/2004.07871/) (2020)
- [Application of Deep Learning-based Interpolation Methods to Nearshore Bathymetry](https://mlsanity.com/paper/2011.09707/) (2020)

## Built on by (most cited first, 15 of 15)

- [Conditional Optimal Transport on Function Spaces](https://mlsanity.com/paper/2311.05672/) (2023)
- [Dynamic Conditional Optimal Transport through Simulation-Free Flows](https://mlsanity.com/paper/2404.04240/) (2024)
- [An Optimal Transport Formulation of Bayes' Law for Nonlinear Filtering Algorithms](https://mlsanity.com/paper/2203.11869/) (2022)
- [Nonlinear Filtering with Brenier Optimal Transport Maps](https://mlsanity.com/paper/2310.13886/) (2023)
- [Solution of physics-based inverse problems using conditional generative adversarial networks with full gradient penalty](https://mlsanity.com/paper/2306.04895/) (2023)
- [Unifying and extending Diffusion Models through PDEs for solving Inverse Problems](https://mlsanity.com/paper/2504.07437/) (2025)
- [Conditional score-based diffusion models for solving inverse problems in mechanics](https://mlsanity.com/paper/2406.13154/) (2024)
- [Generative Algorithms for Fusion of Physics-Based Wildfire Spread Models with Satellite Data for Initializing Wildfire Forecasts](https://mlsanity.com/paper/2309.02615/) (2023)
- [Deep Learning and Computational Physics (Lecture Notes)](https://mlsanity.com/paper/2301.00942/) (2023)
- [Segmenting mechanically heterogeneous domains via unsupervised learning](https://mlsanity.com/paper/2308.15697/) (2023)
- [Generative Algorithms for Wildfire Progression Reconstruction from Multi-Modal Satellite Active Fire Measurements and Terrain Height](https://mlsanity.com/paper/2506.10404/) (2025)
- [Conditional flow matching for physics-constrained inverse problems with finite training data](https://mlsanity.com/paper/2603.14135/) (2026)
- [Learning end-to-end inversion of circular Radon transforms in the partial radial setup](https://mlsanity.com/paper/2308.14144/) (2023)
- [MoRF-AST: Calibrated Probabilistic Virtual Sensing for Structural Monitoring under Changing Operating Conditions](https://mlsanity.com/paper/2608.24531/) (2026)
- [Multi-Dataset Inverse Problem Solving with Distributed Generative AI](https://mlsanity.com/paper/2608.26283/) (2026)

## Abstract (arXiv)

In this work, we train conditional Wasserstein generative adversarial networks to effectively sample from the posterior of physics-based Bayesian inference problems. The generator is constructed using a U-Net architecture, with the latent information injected using conditional instance normalization. The former facilitates a multiscale inverse map, while the latter enables the decoupling of the latent space dimension from the dimension of the measurement, and introduces stochasticity at all scales of the U-Net. We solve PDE-based inverse problems to demonstrate the performance of our approach in quantifying the uncertainty in the inferred field. Further, we show the generator can learn inverse maps which are local in nature, which in turn promotes generalizability when testing with out-of-distribution samples.