# Physics-aware Reduced-order Modeling of Transonic Flow via β-Variational Autoencoder

arXiv: https://arxiv.org/abs/2205.00608 · HTML: https://mlsanity.com/paper/2205.00608/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 46 references that are in the map.
- First posted on arXiv 2 May 2022.

## Builds on (most cited first, 10 of 10)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [From Variational to Deterministic Autoencoders](https://mlsanity.com/paper/1903.12436/) (2019)
- [Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows](https://mlsanity.com/paper/2109.01514/) (2021)
- [Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows](https://mlsanity.com/paper/2007.00936/) (2020)
- [Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques](https://mlsanity.com/paper/2107.11460/) (2021)
- [A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling](https://mlsanity.com/paper/2110.03442/) (2021)
- [Inverse design optimization framework via a two-step deep learning approach: application to a wind turbine airfoil](https://mlsanity.com/paper/2108.08500/) (2021)

## Built on by (most cited first, 15 of 15)

- [Data-Driven Physics-Informed Neural Networks: A Digital Twin Perspective](https://mlsanity.com/paper/2401.08667/) (2024)
- [Residual-based Attention Physics-informed Neural Networks for Spatio-Temporal Ageing Assessment of Transformers Operated in Renewable Power Plants](https://mlsanity.com/paper/2405.06443/) (2024)
- [Towards aerodynamic surrogate modeling based on β-variational autoencoders](https://mlsanity.com/paper/2408.04969/) (2024)
- [Data-Efficient Deep Operator Network for Unsteady Flow: A Multi-Fidelity Approach with Physics-Guided Subsampling](https://mlsanity.com/paper/2503.17941/) (2025)
- [Enhancing Graph U-Nets for Mesh-Agnostic Spatio-Temporal Flow Prediction](https://mlsanity.com/paper/2406.03789/) (2024)
- [Towards Reliable Uncertainty Quantification via Deep Ensembles in Multi-output Regression Task](https://mlsanity.com/paper/2303.16210/) (2023)
- [Data-driven Nonlinear Parametric Model Order Reduction Framework using Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2307.06816/) (2023)
- [Physics-Assisted Reduced-Order Modeling for Identifying Dominant Features of Transonic Buffet](https://mlsanity.com/paper/2305.13644/) (2023)
- [Disentangled Latent Spaces for Reduced Order Models using Deterministic Autoencoders](https://mlsanity.com/paper/2502.14679/) (2025)
- [Point-wise Diffusion Models for Physical Systems with Shape Variations: Application to Spatio-temporal and Large-scale system](https://mlsanity.com/paper/2508.01230/) (2025)
- [Adjoint-based shape optimization of a ship hull using a Conditional Variational Autoencoder (CVAE) assisted propulsion surrogate model](https://mlsanity.com/paper/2602.14907/) (2026)
- [Compact and Intuitive Airfoil Parameterization Method through Physics-aware Variational Autoencoder](https://mlsanity.com/paper/2311.10921/) (2023)
- [Physically Interpretable Representation Learning with Gaussian Mixture Variational AutoEncoder (GM-VAE)](https://mlsanity.com/paper/2511.21883/) (2025)
- [Conditional Neural Field based Reduced Order Model for Dynamic Ditching Load Prediction](https://mlsanity.com/paper/2605.21499/) (2026)
- [HI-MeshGraphNets: Efficient and Accurate Mesh-based Physics Learning with Hierarchical Multi-scale Graph Neural Networks](https://mlsanity.com/paper/2608.13827/) (2026)

## Abstract (arXiv)

Autoencoder-based reduced-order modeling (ROM) has recently attracted significant attention, owing to its ability to capture underlying nonlinear features. However, two critical drawbacks severely undermine its scalability to various physical applications: entangled and therefore uninterpretable latent variables (LVs) and the blindfold determination of latent space dimension. In this regard, this study proposes the physics-aware ROM using only interpretable and information-intensive LVs extracted by β-variational autoencoder, which are referred to as physics-aware LVs throughout this paper. To extract these LVs, their independence and information intensity are quantitatively scrutinized in a two-dimensional transonic flow benchmark problem. Then, the physical meanings of the physics-aware LVs are thoroughly investigated and we confirmed that with appropriate hyperparameter β, they actually correspond to the generating factors of the training dataset, Mach number and angle of attack. To the best of the authors' knowledge, our work is the first to practically confirm that β-variational autoencoder can automatically extract the physical generating factors in the field of applied physics. Finally, physics-aware ROM, which utilizes only physics-aware LVs, is compared with conventional ROMs, and its validity and efficiency are successfully verified.