# Temporally-Consistent Bilinearly Recurrent Autoencoders for Control Systems

arXiv: https://arxiv.org/abs/2503.19085 · HTML: https://mlsanity.com/paper/2503.19085/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2025.

## Built on by (most cited first, 3 of 3)

- [LiDAR-BIND-T: Improved and Temporally Consistent Sensor Modality Translation and Fusion for Robotic Applications](https://mlsanity.com/paper/2509.05728/) (2025)
- [Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems](https://mlsanity.com/paper/2604.12103/) (2026)
- [Learning Control-Affine Reduced-Order Models via Autoencoders](https://mlsanity.com/paper/2606.05045/) (2026)

## Abstract (arXiv)

This paper introduces the temporally-consistent bilinearly recurrent autoencoder (tcBLRAN), a Koopman operator based neural network architecture for modeling a control-affine nonlinear control system. The proposed method extends traditional Koopman autoencoders (KAE) by incorporating bilinear recurrent dynamics that are consistent across predictions, enabling accurate long-term forecasting for control-affine systems. This overcomes the roadblock that KAEs face when encountered with limited and noisy training datasets, resulting in a lack of generalizability due to inconsistency in training data. Through a blend of deep learning and dynamical systems theory, tcBLRAN demonstrates superior performance in capturing complex behaviors and control systems dynamics, providing a superior data-driven modeling technique for control systems and outperforming the state-of-the-art Koopman bilinear form (KBF) learned by autoencoder networks.