Controlling the evolution of complex physical systems is a fundamental task across science and engineering. Classical techniques suffer from limited applicability or huge computational costs. On the other hand, recent deep learning and reinforcement learning-based approaches often struggle to optimize long-term control sequences under the constraints of system dynamics. In this work, we introduce Diffusion Physical systems Control (DiffPhyCon), a new class of method to address the physical systems control problem. DiffPhyCon excels by simultaneously minimizing both the learned generative energy function and the predefined control objectives across the entire trajectory and control sequence. Thus, it can explore globally and plan near-optimal control sequences. Moreover, we enhance DiffPhyCon with prior reweighting, enabling the discovery of control sequences that significantly deviate from the training distribution. We test our method on three tasks: 1D Burgers' equation, 2D jellyfish movement control, and 2D high-dimensional smoke control, where our generated jellyfish dataset is released as a benchmark for complex physical system control research. Our method outperforms widely applied classical approaches and state-of-the-art deep learning and reinforcement learning methods. Notably, DiffPhyCon unveils an intriguing fast-close-slow-open pattern observed in the jellyfish, aligning with established findings in the field of fluid dynamics. The project website, jellyfish dataset, and code can be found at https://github.com/AI4Science-WestlakeU/diffphycon.

翻译：控制复杂物理系统的演化是科学与工程领域的一项基础任务。经典方法存在适用性有限或计算成本高昂的问题。另一方面，近期基于深度学习和强化学习的方法往往难以在系统动力学约束下优化长期控制序列。本文提出扩散物理系统控制（DiffPhyCon），一种解决物理系统控制问题的新方法。DiffPhyCon通过同时最小化整个轨迹与控制序列上的学习生成能量函数和预定义控制目标而表现出色，从而能够进行全局探索并规划接近最优的控制序列。此外，我们通过先验重加权技术增强DiffPhyCon，使其能够发现显著偏离训练分布的控制序列。我们在三个任务上测试了该方法：一维Burgers方程、二维水母运动控制和二维高维烟雾控制，其中我们生成的水母数据集已作为复杂物理系统控制研究的基准发布。我们的方法优于广泛应用的经典方法以及最先进的深度学习和强化学习方法。值得注意的是，DiffPhyCon揭示了水母运动中一种有趣的"快速闭合-缓慢张开"模式，这与流体动力学领域的已有发现相一致。项目网站、水母数据集及代码可通过 https://github.com/AI4Science-WestlakeU/diffphycon 获取。