# Learning Control-Affine Reduced-Order Models via Autoencoders

arXiv: https://arxiv.org/abs/2606.05045 · HTML: https://mlsanity.com/paper/2606.05045/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 42 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders](https://mlsanity.com/paper/2201.05136/) (2022)
- [Data-Driven Reduced-Order Modeling of Spatiotemporal Chaos with Neural Ordinary Differential Equations](https://mlsanity.com/paper/2109.00060/) (2021)
- [Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants](https://mlsanity.com/paper/2211.10575/) (2022)
- [Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2501.13329/) (2025)
- [Data-Driven Model Predictive Control using Interpolated Koopman Generators](https://mlsanity.com/paper/2003.07094/) (2020)
- [Learning deep dynamical models from image pixels](https://mlsanity.com/paper/1410.7550/) (2014)
- [Non-linear State-space Model Identification from Video Data using Deep Encoders](https://mlsanity.com/paper/2012.07721/) (2020)
- [Temporally-Consistent Bilinearly Recurrent Autoencoders for Control Systems](https://mlsanity.com/paper/2503.19085/) (2025)
- [Disentangled Latent Spaces for Reduced Order Models using Deterministic Autoencoders](https://mlsanity.com/paper/2502.14679/) (2025)
- [Estimating flow fields with Reduced Order Models](https://mlsanity.com/paper/2202.05736/) (2022)
- [A Feedback Linearized Model Predictive Control Strategy for Input-Constrained Self-Driving Cars](https://mlsanity.com/paper/2405.01753/) (2024)

## Abstract (arXiv)

We present in this paper a framework for the identification of control-affine reduced-order models (ROMs). The proposed method utilizes autoencoders (AEs) to transform the high-dimensional states, and potentially the high-dimensional inputs, into reduced latent ones suitable for control-affine state-space dynamics. This is achieved by simultaneous training of the AE and the state-space model. In addition, we extend the discrete ROM formulation to a sequence-based model, which processes state and input histories to improve prediction accuracy while preserving the control-affine structure. We motivate our framework by applying feedback linearization to the derived models, and we present guidelines for its efficient use. The proposed framework is assessed on two numerical examples and its performance is compared to a baseline model, where the AE identifies a latent space with linear state-space dynamics. The assessment involves evaluating the prediction accuracy of the ROM on test data and its effectiveness in controlling the system to a desired state or trajectory.