这篇论文用SHRED-ROM实现高维动力系统实时控制，只需少量传感器和专家示例，比传统方法快很多。
论文提出SHRED-ROM方法，利用浅循环解码器网络（SHRED）进行降阶建模，实现高维参数化动力学系统的实时闭环控制。该方法仅需有限传感器读数，通过少量专家示范样本训练，即可在新场景中模仿专家行为并输出分布式控制动作，缓解维度灾难。SHRED-ROM还合成传感器预测器在潜在空间闭环，有效应对传感器故障或延迟。在参数密度控制和流体流动控制两个高维案例上验证了性能。
Real-time optimal control with shallow recurrent decoder networks
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.