CL-DiffPhyCon: Closed-loop Diffusion Control of Complex Physical Systems

TL;DR

The work presents CL-DiffPhyCon, a closed-loop diffusion control framework that enables real-time control of complex physical systems via an asynchronous denoising scheme. By decoupling denoising across physical-time steps and using separate initializing and transition diffusion models, the method samples control signals conditioned on current system feedback with substantially reduced computational cost, and it can be further accelerated with DDIM. Empirical results on 1D Burgers' equation and 2D incompressible fluid control demonstrate superior control performance and notable sampling efficiency gains over strong baselines, including diffusion-based methods. This approach advances practical diffusion-based control by delivering fully closed-loop operation with improved efficiency, making it suitable for high-dimensional, nonlinear physical systems.

Abstract

The control problems of complex physical systems have broad applications in science and engineering. Previous studies have shown that generative control methods based on diffusion models offer significant advantages for solving these problems. However, existing generative control approaches face challenges in both performance and efficiency when extended to the closed-loop setting, which is essential for effective control. In this paper, we propose an efficient Closed-Loop Diffusion method for Physical systems Control (CL-DiffPhyCon). By employing an asynchronous denoising framework for different physical time steps, CL-DiffPhyCon generates control signals conditioned on real-time feedback from the system with significantly reduced computational cost during sampling. Additionally, the control process could be further accelerated by incorporating fast sampling techniques, such as DDIM. We evaluate CL-DiffPhyCon on two tasks: 1D Burgers' equation control and 2D incompressible fluid control. The results demonstrate that CL-DiffPhyCon achieves superior control performance with significant improvements in sampling efficiency. The code can be found at https://github.com/AI4Science-WestlakeU/CL_DiffPhyCon.

Figures (16)

• Figure 1: Advantages of our CL-DiffPhyCon (right) over previous diffusion control methods (left and middle). The diffusion model horizon is denoted as $H$ and the total number of diffusion steps is $T$. By employing an asynchronous denoising framework, our method could achieve closed-loop control and accelerate the sampling process significantly. The notation DiffPhyCon-$h$ means conducting a full sampling process including $T$ denoising steps every $h$ physical time steps.
• Figure 2: CL-DiffPhyCon for closed-loop control. First, it uses the synchronous diffusion model for initialization. Then, it uses the asynchronous diffusion model for iterative control. Sampling of each control signal is based on the latest state feedback from the system dynamics.
• Figure 3: Visual comparisons between CL-DiffPhyCon and best baselines on 2D fluid control under fixed map (top) and random map (bottom) evaluation modes, respectively.
• Figure 4: Illustration of partial observation and control. Blue represents the position observed by sensors, and red represents the position that actuators are able to control. The region filled entirely with blue and red indicates that all spatial regions can be observed and controlled, respectively. The vertical line indicates where there are sensors and actuators in that spatial position.
• Figure 5: Illustration of the 2D incompressible fluid control task settings. In the large domain control setting (middle), control signals are applied to the peripheral green regions surrounding the obstacles. In the boundary control setting (right), control signals are limited to the green cells within the four exits. Two evaluation modes are used: fixed map (top) for in-distribution testing and random map (bottom) for out-of-distribution testing.

Theorems & Definitions (6)

• Theorem 1
• Proposition 1
• proof : Proof of Theorem \ref{['prop:1']}
• proof : Proof of Proposition \ref{['prop:2']}
• Proposition 2
• proof : Proof of Proposition \ref{['prop:3']}