# Adversarial Disentanglement by Backpropagation with Physics-Informed Variational Autoencoder

arXiv: https://arxiv.org/abs/2506.13658 · HTML: https://mlsanity.com/paper/2506.13658/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 78 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 30 of 48)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Learning Robust Representations via Multi-View Information Bottleneck](https://mlsanity.com/paper/2002.07017/) (2020)
- [Recent Advances in Autoencoder-Based Representation Learning](https://mlsanity.com/paper/1812.05069/) (2018)
- [Information Dropout: Learning Optimal Representations Through Noisy Computation](https://mlsanity.com/paper/1611.01353/) (2016)
- [InfoVAE: Information Maximizing Variational Autoencoders](https://mlsanity.com/paper/1706.02262/) (2017)
- [DIVA: Domain Invariant Variational Autoencoders](https://mlsanity.com/paper/1905.10427/) (2019)
- [Invariant Representations without Adversarial Training](https://mlsanity.com/paper/1805.09458/) (2018)
- [The Conditional Entropy Bottleneck](https://mlsanity.com/paper/2002.05379/) (2020)
- [Learning Disentangled Representations with Semi-Supervised Deep Generative Models](https://mlsanity.com/paper/1706.00400/) (2017)
- [Structured Disentangled Representations](https://mlsanity.com/paper/1804.02086/) (2018)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Stabilizing Generative Adversarial Networks: A Survey](https://mlsanity.com/paper/1910.00927/) (2019)
- [Guided Variational Autoencoder for Disentanglement Learning](https://mlsanity.com/paper/2004.01255/) (2020)
- [Information Constraints on Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1805.08672/) (2018)
- [Distributed Variational Representation Learning](https://mlsanity.com/paper/1807.04193/) (2018)

## Built on by (most cited first, 2 of 2)

- [Can Transformers overcome the lack of data in the simulation of history-dependent flows?](https://mlsanity.com/paper/2512.16305/) (2025)
- [In-Context Residual Calibration for Uncertainty Quantification of Energy Time Series over Graphs](https://mlsanity.com/paper/2606.31804/) (2026)

## Abstract (arXiv)

Inference and prediction under partial knowledge of a physical system is challenging, particularly when multiple confounding sources influence the measured response. Explicitly accounting for these influences in physics-based models is often infeasible due to epistemic uncertainty, cost, or time constraints, resulting in models that fail to accurately describe the behavior of the system. On the other hand, data-driven machine learning models such as variational autoencoders are not guaranteed to identify a parsimonious representation. As a result, they can suffer from poor generalization performance and reconstruction accuracy in the regime of limited and noisy data. We propose a physics-informed variational autoencoder architecture that combines the interpretability of physics-based models with the flexibility of data-driven models. To promote disentanglement of the known physics and confounding influences, the latent space is partitioned into physically meaningful variables that parametrize a physics-based model, and data-driven variables that capture variability in the domain and class of the physical system. The encoder is coupled with a decoder that integrates physics-based and data-driven components, and constrained by an adversarial training objective that prevents the data-driven components from overriding the known physics, ensuring that the physics-grounded latent variables remain interpretable. We demonstrate that the model is able to disentangle features of the input signal and separate the known physics from confounding influences using supervision in the form of class and domain observables. The model is evaluated on a series of synthetic case studies relevant to engineering structures, demonstrating the feasibility of the proposed approach.