# Physics-informed Variational Autoencoders for Improved Robustness to Environmental Factors of Variation

arXiv: https://arxiv.org/abs/2210.10418 · HTML: https://mlsanity.com/paper/2210.10418/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 56 references that are in the map.
- First posted on arXiv 19 Oct 2022.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Deep Convolutional Inverse Graphics Network](https://mlsanity.com/paper/1503.03167/) (2015)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [Learning Disentangled Joint Continuous and Discrete Representations](https://mlsanity.com/paper/1804.00104/) (2018)
- [Bias and Generalization in Deep Generative Models: An Empirical Study](https://mlsanity.com/paper/1811.03259/) (2018)
- [Semi-Supervised Learning with Normalizing Flows](https://mlsanity.com/paper/1912.13025/) (2019)
- [Measuring Disentanglement: A Review of Metrics](https://mlsanity.com/paper/2012.09276/) (2020)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Guided Variational Autoencoder for Disentanglement Learning](https://mlsanity.com/paper/2004.01255/) (2020)
- [Deep Learning for Classification of Hyperspectral Data: A Comparative Review](https://mlsanity.com/paper/1904.10674/) (2019)
- [Dirichlet Variational Autoencoder](https://mlsanity.com/paper/1901.02739/) (2019)
- [Semi-Supervised Semantic Segmentation in Earth Observation: The MiniFrance Suite, Dataset Analysis and Multi-task Network Study](https://mlsanity.com/paper/2010.07830/) (2020)
- [Generative ODE Modeling with Known Unknowns](https://mlsanity.com/paper/2003.10775/) (2020)
- [Early Visual Concept Learning with Unsupervised Deep Learning](https://mlsanity.com/paper/1606.05579/) (2016)
- [Unsupervised physics-informed disentanglement of multimodal data for high-throughput scientific discovery](https://mlsanity.com/paper/2202.03242/) (2022)
- [Dirichlet Variational Autoencoder for Text Modeling](https://mlsanity.com/paper/1811.00135/) (2018)
- [Self-supervised Learning with Physics-aware Neural Networks I: Galaxy Model Fitting](https://mlsanity.com/paper/1907.03957/) (2019)
- [Disentangling Generative Factors of Physical Fields Using Variational Autoencoders](https://mlsanity.com/paper/2109.07399/) (2021)
- [Guiding InfoGAN with Semi-Supervision](https://mlsanity.com/paper/1707.04487/) (2017)
- [Thermodynamic Consistent Neural Networks for Learning Material Interfacial Mechanics](https://mlsanity.com/paper/2011.14172/) (2020)

## Built on by (most cited first, 4 of 4)

- [In-Field Mapping of Grape Yield and Quality with Illumination-Invariant Deep Learning](https://mlsanity.com/paper/2510.04864/) (2025)
- [Physically-Grounded Goal Imagination: Physics-Informed Variational Autoencoder for Self-Supervised Reinforcement Learning](https://mlsanity.com/paper/2511.06745/) (2025)
- [Bayesian Inverse Games with High-Dimensional Multi-Modal Observations](https://mlsanity.com/paper/2601.00696/) (2026)
- [Sharpness-Aware Hybrid Model Learning for Architecture-Agnostic Parameter Estimation](https://mlsanity.com/paper/2602.06837/) (2026)

## Abstract (arXiv)

The combination of machine learning models with physical models is a recent research path to learn robust data representations. In this paper, we introduce p3VAE, a variational autoencoder that integrates prior physical knowledge about the latent factors of variation that are related to the data acquisition conditions. p3VAE combines standard neural network layers with non-trainable physics layers in order to partially ground the latent space to physical variables. We introduce a semi-supervised learning algorithm that strikes a balance between the machine learning part and the physics part. Experiments on simulated and real data sets demonstrate the benefits of our framework against competing physics-informed and conventional machine learning models, in terms of extrapolation capabilities and interpretability. In particular, we show that p3VAE naturally has interesting disentanglement capabilities. Our code and data have been made publicly available at https://github.com/Romain3Ch216/p3VAE.