mlsanityData to 7 Oct 2026

Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling

arXiv 2102.13156 ↗First posted 25 Feb 2021cs.LG stat.MLcited by 59

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Abstract (arXiv)

Integrating physics models within machine learning models holds considerable promise toward learning robust models with improved interpretability and abilities to extrapolate. In this work, we focus on the integration of incomplete physics models into deep generative models. In particular, we introduce an architecture of variational autoencoders (VAEs) in which a part of the latent space is grounded by physics. A key technical challenge is to strike a balance between the incomplete physics and trainable components such as neural networks for ensuring that the physics part is used in a meaningful manner. To this end, we propose a regularized learning method that controls the effect of the trainable components and preserves the semantics of the physics-based latent variables as intended. We not only demonstrate generative performance improvements over a set of synthetic and real-world datasets, but we also show that we learn robust models that can consistently extrapolate beyond the training distribution in a meaningful manner. Moreover, we show that we can control the generative process in an interpretable manner.

Key facts. Cited by 59 papers in the map (data through 7 Oct 2026). Builds on 65 of its 118 references that are in the map. First posted on arXiv 25 Feb 2021.

Builds on

65 of 118 references.

References · 65

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38 more
  1. 2021Towards Causal Representation Learningcited by 207
  2. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 205
  3. 2019Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systemscited by 203
  4. 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 201
  5. 2020Disentangling Physical Dynamics from Unknown Factors for Unsupervised Video Predictioncited by 192
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  8. 2016Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Datacited by 154
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  13. 2017Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modelingcited by 130
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  17. 2020Augmenting Physical Models with Deep Networks for Complex Dynamics Forecastingcited by 93
  18. 2020NeuralSim: Augmenting Differentiable Simulators with Neural Networkscited by 77
  19. 2016Label-Free Supervision of Neural Networks with Physics and Domain Knowledgecited by 74
  20. 2018Gaussian Process Prior Variational Autoencoderscited by 72
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  22. 2019Physics-as-Inverse-Graphics: Unsupervised Physical Parameter Estimation from Videocited by 43
  23. 2019Physics-guided Convolutional Neural Network (PhyCNN) for Data-driven Seismic Response Modelingcited by 40
  24. 2018Augmenting Physical Simulators with Stochastic Neural Networks: Case Study of Planar Pushing and Bouncingcited by 36
  25. 2019Variational Integrator Networks for Physically Structured Embeddingscited by 36
  26. 2020Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physicscited by 36
  27. 2020Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanicscited by 32
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50 most cited of 65 All 65 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 10; 2023: 12; 2024: 13; 2025: 12; 2026: 11.

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  1. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  2. 2023Physics-Informed Computer Vision: A Review and Perspectivescited by 28
  3. 2024Addressing Misspecification in Simulation-based Inference through Data-driven Calibrationcited by 26
  4. 2022Neural Implicit Representations for Physical Parameter Inference from a Single Videocited by 19
  5. 2022Fully probabilistic deep models for forward and inverse problems in parametric PDEscited by 19
  6. 2022Robust Hybrid Learning With Expert Augmentationcited by 17
  7. 2024Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Responsecited by 13
  8. 2024Diffusion Prior-Based Amortized Variational Inference for Noisy Inverse Problemscited by 13
  9. 2024Learning Physics From Video: Unsupervised Physical Parameter Estimation for Continuous Dynamical Systemscited by 13
  10. 2024Automatically Learning Hybrid Digital Twins of Dynamical Systemscited by 13
  11. 2024The Causal Chambers: Real Physical Systems as a Testbed for AI Methodologycited by 12
  12. 2022Estimating counterfactual treatment outcomes over time in complex multiagent scenarioscited by 11
38 more
  1. 2024Physics-Enhanced Machine Learning: a position paper for dynamical systems investigationscited by 11
  2. 2022Knowledge-augmented Deep Learning and Its Applications: A Surveycited by 10
  3. 2021Disentangled Generative Models for Robust Prediction of System Dynamicscited by 8
  4. 2023Random Grid Neural Processes for Parametric Partial Differential Equationscited by 8
  5. 2023HyperSINDy: Deep Generative Modeling of Nonlinear Stochastic Governing Equationscited by 7
  6. 2024GEPS: Boosting Generalization in Parametric PDE Neural Solvers through Adaptive Conditioningcited by 7
  7. 2022Deep Grey-Box Modeling With Adaptive Data-Driven Models Toward Trustworthy Estimation of Theory-Driven Modelscited by 6
  8. 2023Dream to Adapt: Meta Reinforcement Learning by Latent Context Imagination and MDP Imaginationcited by 6
  9. 2024Generating Physical Dynamics under Priorscited by 6
  10. 2022Physics-informed Variational Autoencoders for Improved Robustness to Environmental Factors of Variationcited by 4
  11. 2025Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamicscited by 4
  12. 2025Inductive Domain Transfer In Misspecified Simulation-Based Inferencecited by 4
  13. 2023Hybrid additive modeling with partial dependence for supervised regression and dynamical systems forecastingcited by 2
  14. 2023DPA-WNO: A gray box model for a class of stochastic mechanics problemcited by 2
  15. 2023Physics-Informed Data Denoising for Real-Life Sensing Systemscited by 2
  16. 2024KAE: Kolmogorov-Arnold Auto-Encoder for Representation Learningcited by 2
  17. 2025Adversarial Disentanglement by Backpropagation with Physics-Informed Variational Autoencodercited by 2
  18. 2025A Generalizable Physics-Enhanced State Space Model for Long-Term Dynamics Forecasting in Complex Environmentscited by 2
  19. 2026Variational Grey-Box Dynamics Matchingcited by 2
  20. 2023Using VAEs to Learn Latent Variables: Observations on Applications in cryo-EMcited by 1
  21. 2023Learning Hybrid Dynamics Models With Simulator-Informed Latent Statescited by 1
  22. 2024Physics-integrated generative modeling using attentive planar normalizing flow based variational autoencodercited by 1
  23. 2024PILA: Physics-Informed Low Rank Augmentation for Interpretable Earth Observationcited by 1
  24. 2025Hybrid Generative Modeling for Incomplete Physics: Deep Grey-Box Meets Optimal Transportcited by 1
  25. 2025Variational Rank Reduction Autoencoders for Generative Thermal Designcited by 1
  26. 2025Flow Matching Calibration for Simulation-Based Inference under Model Misspecificationcited by 1
  27. 2025Inferring Optical Tissue Properties from Photoplethysmography using Hybrid Amortized Inferencecited by 1
  28. 2022Quantitative Imaging Principles Improves Medical Image Learningcited by 0
  29. 2022Modeling Nonlinear Dynamics in Continuous Time with Inductive Biases on Decay Rates and/or Frequenciescited by 0
  30. 2023Compact and Intuitive Airfoil Parameterization Method through Physics-aware Variational Autoencodercited by 0
  31. 2023Interpretable Mechanistic Representations for Meal-level Glycemic Control in the Wildcited by 0
  32. 2023Deep Learning with Physics Priors as Generalized Regularizerscited by 0
  33. 2024Towards detailed and interpretable hybrid modeling of continental-scale bird migrationcited by 0
  34. 2025Biomechanical Constraints Assimilation in Deep-Learning Image Registration: Application to sliding and locally rigid deformationscited by 0
  35. 2025PIGPVAE: Physics-Informed Gaussian Process Variational Autoencoderscited by 0
  36. 2025Learning Mechanistic Subtypes of Neurodegeneration with a Physics-Informed Variational Autoencoder Mixture Modelcited by 0
  37. 2025Physically-Grounded Goal Imagination: Physics-Informed Variational Autoencoder for Self-Supervised Reinforcement Learningcited by 0
  38. 2026Bayesian Inverse Games with High-Dimensional Multi-Modal Observationscited by 0

50 most cited of 59 All 59 (JSON)