Wei Long

Long Wei, Haodong Feng, Yuchen Yang et al.

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.

Peiyan Hu, Xiaowei Qian, Wenhao Deng et al.

The application of deep learning for partial differential equation (PDE)-constrained control is gaining increasing attention. However, existing methods rarely consider safety requirements crucial in real-world applications. To address this limitation, we propose Safe Diffusion Models for PDE Control (SafeDiffCon), which introduce the uncertainty quantile as model uncertainty quantification to achieve optimal control under safety constraints through both post-training and inference phases. Firstly, our approach post-trains a pre-trained diffusion model to generate control sequences that better satisfy safety constraints while achieving improved control objectives via a reweighted diffusion loss, which incorporates the uncertainty quantile estimated using conformal prediction. Secondly, during inference, the diffusion model dynamically adjusts both its generation process and parameters through iterative guidance and fine-tuning, conditioned on control targets while simultaneously integrating the estimated uncertainty quantile. We evaluate SafeDiffCon on three control tasks: 1D Burgers' equation, 2D incompressible fluid, and controlled nuclear fusion problem. Results demonstrate that SafeDiffCon is the only method that satisfies all safety constraints, whereas other classical and deep learning baselines fail. Furthermore, while adhering to safety constraints, SafeDiffCon achieves the best control performance. The code can be found at https://github.com/AI4Science-WestlakeU/safediffcon.

Wei Long, Xingyu Zhou, Leheng Zhang et al.

Transformer-based methods have achieved remarkable results in image super-resolution tasks because they can capture non-local dependencies in low-quality input images. However, this feature-intensive modeling approach is computationally expensive because it calculates the similarities between numerous features that are irrelevant to the query features when obtaining attention weights. These unnecessary similarity calculations not only degrade the reconstruction performance but also introduce significant computational overhead. How to accurately identify the features that are important to the current query features and avoid similarity calculations between irrelevant features remains an urgent problem. To address this issue, we propose a novel and effective Progressive Focused Transformer (PFT) that links all isolated attention maps in the network through Progressive Focused Attention (PFA) to focus attention on the most important tokens. PFA not only enables the network to capture more critical similar features, but also significantly reduces the computational cost of the overall network by filtering out irrelevant features before calculating similarities. Extensive experiments demonstrate the effectiveness of the proposed method, achieving state-of-the-art performance on various single image super-resolution benchmarks.