# Real-time optimal control with shallow recurrent decoder networks

arXiv: https://arxiv.org/abs/2607.19302 · HTML: https://mlsanity.com/paper/2607.19302/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 67 references that are in the map.
- First posted on arXiv 21 Jul 2026.

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

- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs](https://mlsanity.com/paper/2001.04001/) (2020)
- [Data-driven approximation of the Koopman generator: Model reduction, system identification, and control](https://mlsanity.com/paper/1909.10638/) (2019)
- [Optimal control of PDEs using physics-informed neural networks](https://mlsanity.com/paper/2111.09880/) (2021)
- [Solving PDE-constrained Control Problems Using Operator Learning](https://mlsanity.com/paper/2111.04941/) (2021)
- [Koopman operator-based model reduction for switched-system control of PDEs](https://mlsanity.com/paper/1710.06759/) (2017)
- [Physics-Informed Neural Nets for Control of Dynamical Systems](https://mlsanity.com/paper/2104.02556/) (2021)
- [Fast PDE-constrained optimization via self-supervised operator learning](https://mlsanity.com/paper/2110.13297/) (2021)
- [Reduced Order Modeling with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2502.10930/) (2025)
- [Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2501.13329/) (2025)
- [Physics-informed neural networks for PDE-constrained optimization and control](https://mlsanity.com/paper/2205.03377/) (2022)
- [An extended physics informed neural network for preliminary analysis of parametric optimal control problems](https://mlsanity.com/paper/2110.13530/) (2021)
- [AONN: An adjoint-oriented neural network method for all-at-once solutions of parametric optimal control problems](https://mlsanity.com/paper/2302.02076/) (2023)
- [Leveraging arbitrary mobile sensor trajectories with shallow recurrent decoder networks for full-state reconstruction](https://mlsanity.com/paper/2307.11793/) (2023)
- [Shallow Recurrent Decoder for Reduced Order Modeling of Plasma Dynamics](https://mlsanity.com/paper/2405.11955/) (2024)
- [Data assimilation and discrepancy modeling with shallow recurrent decoders](https://mlsanity.com/paper/2512.01170/) (2025)
- [Model Reduction For Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering](https://mlsanity.com/paper/1710.01640/) (2017)
- [On the Universal Transformation of Data-Driven Models to Control Systems](https://mlsanity.com/paper/2102.04722/) (2021)
- [A PINN approach for the online identification and control of unknown PDEs](https://mlsanity.com/paper/2408.03456/) (2024)
- [Feedback control of nonlinear PDEs using data-efficient reduced order models based on the Koopman operator](https://mlsanity.com/paper/1806.09898/) (2018)
- [Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order models](https://mlsanity.com/paper/2409.05709/) (2024)
- [T-SHRED: Symbolic Regression for Regularization and Model Discovery with Transformer Shallow Recurrent Decoders](https://mlsanity.com/paper/2506.15881/) (2025)
- [Asymptotic Stability of POD based Model Predictive Control for a semilinear parabolic PDE](https://mlsanity.com/paper/1312.2145/) (2013)
- [HJB-POD feedback control for Navier-Stokes equations](https://mlsanity.com/paper/1405.1209/) (2014)
- [Feedback control of parametrized PDEs via model order reduction and dynamic programming principle](https://mlsanity.com/paper/1810.00021/) (2018)
- [PySHRED: A Python package for SHallow REcurrent Decoding for sparse sensing, model reduction and scientific discovery](https://mlsanity.com/paper/2507.20954/) (2025)
- [UQ-SHRED: uncertainty quantification of shallow recurrent decoder networks for sparse sensing via engression](https://mlsanity.com/paper/2604.01305/) (2026)

## Abstract (arXiv)

Controlling dynamical systems in real-time across multiple scenarios is critical to enabling adaptive control strategies, ensuring stability and efficiency. However, to tailor control actions in response to varying scenarios, traditional optimal control problems typically require several system simulations, which are often computationally demanding due to the high-dimensionality of the underlying spatio-temporal dynamics. In this work, we exploit SHallow REcurrent Decoder networks-based Reduced Order Modeling (SHRED-ROM) to synthesize a real-time closed-loop controller for high-dimensional and parametric dynamics, relying solely on limited state sensor readings. After training the model on a few optimal examples given by an expert demonstrator, SHRED-ROM mimics the expert behavior with effective distributed control actions in new scenarios, alleviating the curse of dimensionality. Moreover, a sensor forecaster is synthesized and used to close the loop at the latent level, thus efficiently mitigating possible sensor failures or delays. The performance of the proposed optimal control strategy is finally assessed on three challenging high-dimensional cases dealing with either parametric density control or fluid flow control.