Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling
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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
- 2013Auto-Encoding Variational Bayescited by 3,980
- 2018Neural Ordinary Differential Equationscited by 3,733
- 2019Hamiltonian Neural Networkscited by 702
- 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 588
- 2019The frontier of simulation-based inferencecited by 490
- 2020Lagrangian Neural Networkscited by 388
- 2015A Recurrent Latent Variable Model for Sequential Datacited by 362
- 2020Universal Differential Equations for Scientific Machine Learningcited by 345
- 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
- 2017PDE-Net: Learning PDEs from Datacited by 304
- 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 233
- 2018PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Networkcited by 208
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- 2021Towards Causal Representation Learningcited by 207
- 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 205
- 2019Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systemscited by 203
- 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 201
- 2020Disentangling Physical Dynamics from Unknown Factors for Unsupervised Video Predictioncited by 192
- 2016Structured Inference Networks for Nonlinear State Space Modelscited by 182
- 2016Theory-guided Data Science: A New Paradigm for Scientific Discovery from Datacited by 169
- 2016Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Datacited by 154
- 2020Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Predictioncited by 137
- 2019Hamiltonian Generative Networkscited by 136
- 2020Model-Based Deep Learningcited by 136
- 2019TossingBot: Learning to Throw Arbitrary Objects with Residual Physicscited by 131
- 2017Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modelingcited by 130
- 2018Disentangled Sequential Autoencodercited by 117
- 2016Sequential Neural Models with Stochastic Layerscited by 115
- 2017Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledgecited by 95
- 2020Augmenting Physical Models with Deep Networks for Complex Dynamics Forecastingcited by 93
- 2020NeuralSim: Augmenting Differentiable Simulators with Neural Networkscited by 77
- 2016Label-Free Supervision of Neural Networks with Physics and Domain Knowledgecited by 74
- 2018Gaussian Process Prior Variational Autoencoderscited by 72
- 2018Physics Guided RNNs for Modeling Dynamical Systems: A Case Study in Simulating Lake Temperature Profilescited by 55
- 2019Physics-as-Inverse-Graphics: Unsupervised Physical Parameter Estimation from Videocited by 43
- 2019Physics-guided Convolutional Neural Network (PhyCNN) for Data-driven Seismic Response Modelingcited by 40
- 2018Augmenting Physical Simulators with Stochastic Neural Networks: Case Study of Planar Pushing and Bouncingcited by 36
- 2019Variational Integrator Networks for Physically Structured Embeddingscited by 36
- 2020Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physicscited by 36
- 2020Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanicscited by 32
- 2020SimGANs: Simulator-Based Generative Adversarial Networks for ECG Synthesis to Improve Deep ECG Classificationcited by 32
- 2020A probabilistic generative model for semi-supervised training of coarse-grained surrogates and enforcing physical constraints through virtual observablescited by 28
- 2021Variational Data Assimilation with a Learned Inverse Observation Operatorcited by 28
- 2020Solving inverse-PDE problems with physics-aware neural networkscited by 27
- 2021SimGAN: Hybrid Simulator Identification for Domain Adaptation via Adversarial Reinforcement Learningcited by 27
- 2019Incorporating physical constraints in a deep probabilistic machine learning framework for coarse-graining dynamical systemscited by 25
- 2020Generative ODE Modeling with Known Unknownscited by 24
- 2021Hybrid FEM-NN models: Combining artificial neural networks with the finite element methodcited by 24
- 2020Physics guided machine learning using simplified theoriescited by 23
- 2020Interpretable Sequence Learning for COVID-19 Forecastingcited by 22
- 2018HybridNet: Integrating Model-based and Data-driven Learning to Predict Evolution of Dynamical Systemscited by 21
50 most cited of 65 All 65 (JSON)
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Citing papers per year: 2021: 1; 2022: 10; 2023: 12; 2024: 13; 2025: 12; 2026: 11.
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- 2026Structured Hybrid Mechanistic Models for Robust Estimation of Time-Dependent Intervention Outcomes11 Feb 2026
- 2026Sharpness-Aware Hybrid Model Learning for Architecture-Agnostic Parameter Estimation6 Feb 2026
- 2026Bayesian Inverse Games with High-Dimensional Multi-Modal Observations2 Jan 2026
- 2025Physically-Grounded Goal Imagination: Physics-Informed Variational Autoencoder for Self-Supervised Reinforcement Learning10 Nov 2025
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- 2025A Generalizable Physics-Enhanced State Space Model for Long-Term Dynamics Forecasting in Complex Environments14 Jul 2025
- 2025Hybrid Generative Modeling for Incomplete Physics: Deep Grey-Box Meets Optimal Transport27 Jun 2025
- 2025Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamics23 Jun 2025
- 2025Adversarial Disentanglement by Backpropagation with Physics-Informed Variational Autoencoder16 Jun 2025
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- 2023Hybrid additive modeling with partial dependence for supervised regression and dynamical systems forecasting5 Jul 2023
- 2023Physics-Informed Computer Vision: A Review and Perspectives29 May 2023
- 2023Using VAEs to Learn Latent Variables: Observations on Applications in cryo-EM13 Mar 2023
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- 2022Fully probabilistic deep models for forward and inverse problems in parametric PDEscited by 19
- 2022Robust Hybrid Learning With Expert Augmentationcited by 17
- 2024Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Responsecited by 13
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- 2024Automatically Learning Hybrid Digital Twins of Dynamical Systemscited by 13
- 2024The Causal Chambers: Real Physical Systems as a Testbed for AI Methodologycited by 12
- 2022Estimating counterfactual treatment outcomes over time in complex multiagent scenarioscited by 11
- 2024Physics-Enhanced Machine Learning: a position paper for dynamical systems investigationscited by 11
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- 2026DT2: Decision-Targeted Digital Twins24 Jun 2026
- 2026HAPI-EP: Towards Hybrid, Adaptive, and Predictive Digital Twins of Cardiac Electrophysiology14 Jun 2026
- 2026APIC: Amortized Physics-Informed Calibration using Neural Processes2 Jun 2026
- 2026Excluding the Target Domain Improves Extrapolation: Deconfounded Hierarchical Physics Constraints8 May 2026
- 2026Structured Hybrid Mechanistic Models for Robust Estimation of Time-Dependent Intervention Outcomes11 Feb 2026
- 2026Sharpness-Aware Hybrid Model Learning for Architecture-Agnostic Parameter Estimation6 Feb 2026
- 2026Bayesian Inverse Games with High-Dimensional Multi-Modal Observations2 Jan 2026
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