mlsanityData to 7 Oct 2026

A Primer on Variational Inference for Physics-Informed Deep Generative Modelling

arXiv 2409.06560 ↗First posted 10 Sep 2024stat.ML cs.LG physics.comp-phcited by 3

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Abstract (arXiv)

Variational inference (VI) is a computationally efficient and scalable methodology for approximate Bayesian inference. It strikes a balance between accuracy of uncertainty quantification and practical tractability. It excels at generative modelling and inversion tasks due to its built-in Bayesian regularisation and flexibility, essential qualities for physics related problems. For such problems, the underlying physical model determines the dependence between variables of interest, which in turn will require a tailored derivation for the central VI learning objective. Furthermore, in many physical inference applications this structure has rich meaning and is essential for accurately capturing the dynamics of interest. In this paper, we provide an accessible and thorough technical introduction to VI for forward and inverse problems, guiding the reader through standard derivations of the VI framework and how it can best be realized through deep learning. We then review and unify recent literature exemplifying the flexibility allowed by VI. This paper is designed for a general scientific audience looking to solve physics-based problems with an emphasis on uncertainty quantification

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 42 of its 81 references that are in the map. First posted on arXiv 10 Sep 2024.

Builds on

42 of 81 references.

References · 42

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2015Variational Inference with Normalizing Flowscited by 2,161
  3. 2016Density estimation using Real NVPcited by 2,029
  4. 2016Variational Inference: A Review for Statisticianscited by 1,466
  5. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  6. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  7. 2013Black Box Variational Inferencecited by 317
  8. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  9. 2017Advances in Variational Inferencecited by 236
  10. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  11. 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 169
  12. 2021Exact imposition of boundary conditions with distance functions in physics-informed deep neural networkscited by 135
30 more
  1. 2018Physics-Informed Generative Adversarial Networks for Stochastic Differential Equationscited by 133
  2. 2017Frequentist Consistency of Variational Bayescited by 60
  3. 2019Generalized Variational Inference: Three arguments for deriving new Posteriorscited by 57
  4. 2021Learning Functional Priors and Posteriors from Data and Physicscited by 37
  5. 2019MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancycited by 35
  6. 2021Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow modelscited by 34
  7. 2019Solving Bayesian Inverse Problems via Variational Autoencoderscited by 32
  8. 2017Training-image based geostatistical inversion using a spatial generative adversarial neural networkcited by 31
  9. 2021Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priorscited by 29
  10. 2020A probabilistic generative model for semi-supervised training of coarse-grained surrogates and enforcing physical constraints through virtual observablescited by 28
  11. 2019Incorporating physical constraints in a deep probabilistic machine learning framework for coarse-graining dynamical systemscited by 25
  12. 2022Reliable amortized variational inference with physics-based latent distribution correctioncited by 25
  13. 2017Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural networkcited by 24
  14. 2022PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equationscited by 20
  15. 2022Mean-field Variational Inference via Wasserstein Gradient Flowcited by 19
  16. 2022Fully probabilistic deep models for forward and inverse problems in parametric PDEscited by 19
  17. 2018Inverse Problems and Data Assimilationcited by 18
  18. 2018Wasserstein Variational Inferencecited by 17
  19. 2022Sliced Wasserstein Variational Inferencecited by 17
  20. 2023A dimension-reduced variational approach for solving physics-based inverse problems using generative adversarial network priors and normalizing flowscited by 12
  21. 2024Efficient Prior Calibration From Indirect Datacited by 11
  22. 2018A Bilevel Approach for Parameter Learning in Inverse Problemscited by 9
  23. 2020Variational Autoencoding of PDE Inverse Problemscited by 9
  24. 2023Random Grid Neural Processes for Parametric Partial Differential Equationscited by 8
  25. 2019A physics-aware, probabilistic machine learning framework for coarse-graining high-dimensional systems in the Small Data regimecited by 7
  26. 2021Variational Inference with NoFAS: Normalizing Flow with Adaptive Surrogate for Computationally Expensive Modelscited by 7
  27. 2024Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous mediacited by 5
  28. 2021Self-supervised optimization of random material microstructures in the small-data regimecited by 4
  29. 2022Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilationcited by 4
  30. 2023VI-DGP: A variational inference method with deep generative prior for solving high-dimensional inverse problemscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 2.

3 papers.

  1. 2025Adversarial Disentanglement by Backpropagation with Physics-Informed Variational Autoencodercited by 2
  2. 2026Hierarchical Inference and Closure Learning via Adaptive Surrogates for ODEs and PDEscited by 0
  3. 2026Generative Priors Conditioned on Natural Language for Bayesian Inversion in PDEscited by 0