mlsanityData to 7 Oct 2026

A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks

arXiv 2105.13136 ↗First posted 27 May 2021cs.LG cs.NA math.NAcited by 30

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Abstract (arXiv)

This work is the first to employ and adapt the image-to-image translation concept based on conditional generative adversarial networks (cGAN) towards learning a forward and an inverse solution operator of partial differential equations (PDEs). Even though the proposed framework could be applied as a surrogate model for the solution of any PDEs, here we focus on steady-state solutions of coupled hydro-mechanical processes in heterogeneous porous media. Strongly heterogeneous material properties, which translate to the heterogeneity of coefficients of the PDEs and discontinuous features in the solutions, require specialized techniques for the forward and inverse solution of these problems. Additionally, parametrization of the spatially heterogeneous coefficients is excessively difficult by using standard reduced order modeling techniques. In this work, we overcome these challenges by employing the image-to-image translation concept to learn the forward and inverse solution operators and utilize a U-Net generator and a patch-based discriminator. Our results show that the proposed data-driven reduced order model has competitive predictive performance capabilities in accuracy and computational efficiency as well as training time requirements compared to state-of-the-art data-driven methods for both forward and inverse problems.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). Builds on 37 of its 130 references that are in the map. First posted on arXiv 27 May 2021.

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37 of 130 references.

References · 37

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25 more
  1. 2019Semantic Image Synthesis with Spatially-Adaptive Normalizationcited by 1,295
  2. 2017High-Resolution Image Synthesis and Semantic Manipulation with Conditional GANscited by 1,176
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  4. 2018Multimodal Unsupervised Image-to-Image Translationcited by 795
  5. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  6. 2019Interpreting the Latent Space of GANs for Semantic Face Editingcited by 691
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  14. 2021The mixed deep energy method for resolving concentration features in finite strain hyperelasticitycited by 28
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  16. 2020Component-wise reduced order model lattice-type structure designcited by 16
  17. 2019Learning to regularize with a variational autoencoder for hydrologic inverse analysiscited by 6
  18. 2021Non-intrusive reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximationcited by 6
  19. 2020Physics-informed Neural Networks for Solving Inverse Problems of Nonlinear Biot's Equations: Batch Trainingcited by 5
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 10; 2023: 7; 2024: 3; 2025: 4; 2026: 1.

30 papers.

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  1. 2022gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identificationcited by 30
  2. 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
  3. 2021Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniquescited by 23
  4. 2023Deep Operator Learning Lessens the Curse of Dimensionality for PDEscited by 18
  5. 2022Thermodynamically Consistent Machine-Learned Internal State Variable Approach for Data-Driven Modeling of Path-Dependent Materialscited by 17
  6. 2022The efficacy and generalizability of conditional GANs for posterior inference in physics-based inverse problemscited by 15
  7. 2024Physics-informed active learning with simultaneous weak-form latent space dynamics identificationcited by 13
  8. 2022Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learningcited by 12
  9. 2021Interval and fuzzy physics-informed neural networks for uncertain fieldscited by 9
  10. 2023Generative Adversarial Reduced Order Modellingcited by 7
  11. 2021Physics-Informed Machine Learning Method for Large-Scale Data Assimilation Problemscited by 6
  12. 2026Out-of-Distribution Generalization for Neural Physics Solverscited by 4
18 more
  1. 2021Uncertainty quantification and inverse modeling for subsurface flow in 3D heterogeneous formations using a theory-guided convolutional encoder-decoder networkcited by 3
  2. 2022Machine Learning in Heterogeneous Porous Materialscited by 3
  3. 2022An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipescited by 3
  4. 2025Generative Learning for Slow Manifolds and Bifurcation Diagramscited by 3
  5. 2021Generative Network-Based Reduced-Order Model for Prediction, Data Assimilation and Uncertainty Quantificationcited by 2
  6. 2022Conditional Generative Models for Simulation of EMG During Naturalistic Movementscited by 2
  7. 2022A generalized machine learning framework for brittle crack problems using transfer learning and graph neural networkscited by 2
  8. 2023Gaussian process regression and conditional Karhunen-Lo'eve models for data assimilation in inverse problemscited by 2
  9. 2024System stabilization with policy optimization on unstable latent manifoldscited by 2
  10. 2025Input Specific Neural Networkscited by 2
  11. 2024Diffusion Model-based Parameter Estimation in Dynamic Power Systemscited by 1
  12. 2025Deep operator network for surrogate modeling of poroelasticity with random permeability fieldscited by 1
  13. 2022Predictive Scale-Bridging Simulations through Active Learningcited by 0
  14. 2023Data-Driven Modeling of an Unsaturated Bentonite Buffer Model Test Under High Temperatures Using an Enhanced Axisymmetric Reproducing Kernel Particle Methodcited by 0
  15. 2023Subsurface Characterization using Ensemble-based Approaches with Deep Generative Modelscited by 0
  16. 2023Progressive reduced order modeling: empowering data-driven modeling with selective knowledge transfercited by 0
  17. 2023Efficient machine-learning surrogates for large-scale geological carbon and energy storagecited by 0
  18. 2025Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Modelcited by 0