Haodong Feng

Long Wei, Peiyan Hu, Ruiqi Feng et al.

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.

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.

Haodong Feng, Yue Wang, Hui Xiang et al.

Deep reinforcement learning (DRL) for fluidic pinball, three individually rotating cylinders in the uniform flow arranged in an equilaterally triangular configuration, can learn the efficient flow control strategies due to the validity of self-learning and data-driven state estimation for complex fluid dynamic problems. In this work, we present a DRL-based real-time feedback strategy to control the hydrodynamic force on fluidic pinball, i.e., force extremum and tracking, from cylinders' rotation. By adequately designing reward functions and encoding historical observations, and after automatic learning of thousands of iterations, the DRL-based control was shown to make reasonable and valid control decisions in nonparametric control parameter space, which is comparable to and even better than the optimal policy found through lengthy brute-force searching. Subsequently, one of these results was analyzed by a machine learning model that enabled us to shed light on the basis of decision-making and physical mechanisms of the force tracking process. The finding from this work can control hydrodynamic force on the operation of fluidic pinball system and potentially pave the way for exploring efficient active flow control strategies in other complex fluid dynamic problems.

Tianrun Gao, Haoren Zheng, Wenhao Deng et al.

Real-world physical systems are inherently complex, often involving the coupling of multiple physics, making their simulation both highly valuable and challenging. Many mainstream approaches face challenges when dealing with decoupled data. Besides, they also suffer from low efficiency and fidelity in strongly coupled spatio-temporal physical systems. Here we propose GenCP, a novel and elegant generative paradigm for coupled multiphysics simulation. By formulating coupled-physics modeling as a probability modeling problem, our key innovation is to integrate probability density evolution in generative modeling with iterative multiphysics coupling, thereby enabling training on data from decoupled simulation and inferring coupled physics during sampling. We also utilize operator-splitting theory in the space of probability evolution to establish error controllability guarantees for this "conditional-to-joint" sampling scheme. We evaluate our paradigm on a synthetic setting and three challenging multi-physics scenarios to demonstrate both principled insight and superior application performance of GenCP. Code is available at this repo: github.com/AI4Science-WestlakeU/GenCP.

Peiyan Hu, Rui Wang, Xiang Zheng et al.

Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these tasks due to their ability to capture long-term dependencies and model high-dimensional states. However, diffusion models typically struggle with handling system states with abrupt changes and generalizing to higher resolutions. In this work, we propose Wavelet Diffusion Neural Operator (WDNO), a novel PDE simulation and control framework that enhances the handling of these complexities. WDNO comprises two key innovations. Firstly, WDNO performs diffusion-based generative modeling in the wavelet domain for the entire trajectory to handle abrupt changes and long-term dependencies effectively. Secondly, to address the issue of poor generalization across different resolutions, which is one of the fundamental tasks in modeling physical systems, we introduce multi-resolution training. We validate WDNO on five physical systems, including 1D advection equation, three challenging physical systems with abrupt changes (1D Burgers' equation, 1D compressible Navier-Stokes equation and 2D incompressible fluid), and a real-world dataset ERA5, which demonstrates superior performance on both simulation and control tasks over state-of-the-art methods, with significant improvements in long-term and detail prediction accuracy. Remarkably, in the challenging context of the 2D high-dimensional and indirect control task aimed at reducing smoke leakage, WDNO reduces the leakage by 78% compared to the second-best baseline. The code can be found at https://github.com/AI4Science-WestlakeU/wdno.git.

Peiyan Hu, Haodong Feng, Hongyuan Liu et al.

Predicting the evolution of complex physical systems remains a central problem in science and engineering. Despite rapid progress in scientific Machine Learning (ML) models, a critical bottleneck is the lack of expensive real-world data, resulting in most current models being trained and validated on simulated data. Beyond limiting the development and evaluation of scientific ML, this gap also hinders research into essential tasks such as sim-to-real transfer. We introduce RealPDEBench, the first benchmark for scientific ML that integrates real-world measurements with paired numerical simulations. RealPDEBench consists of five datasets, three tasks, eight metrics, and ten baselines. We first present five real-world measured datasets with paired simulated datasets across different complex physical systems. We further define three tasks, which allow comparisons between real-world and simulated data, and facilitate the development of methods to bridge the two. Moreover, we design eight evaluation metrics, spanning data-oriented and physics-oriented metrics, and finally benchmark ten representative baselines, including state-of-the-art models, pretrained PDE foundation models, and a traditional method. Experiments reveal significant discrepancies between simulated and real-world data, while showing that pretraining with simulated data consistently improves both accuracy and convergence. In this work, we hope to provide insights from real-world data, advancing scientific ML toward bridging the sim-to-real gap and real-world deployment. Our benchmark, datasets, and instructions are available at https://realpdebench.github.io/.

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.

Haodong Feng, Lugang Ye, Dixia Fan

The integration of artificial intelligence into experimental fluid mechanics promises to accelerate discovery, yet most AI applications remain narrowly focused on numerical studies. This work proposes an AI Fluid Scientist framework that autonomously executes the complete experimental workflow: hypothesis generation, experimental design, robotic execution, data analysis, and manuscript preparation. We validate this through investigation of vortex-induced vibration (VIV) and wake-induced vibration (WIV) in tandem cylinders. Our work has four key contributions: (1) A computer-controlled circulating water tunnel (CWT) with programmatic control of flow velocity, cylinder position, and forcing parameters (vibration frequency and amplitude) with data acquisition (displacement, force, and torque). (2) Automated experiments reproduce literature benchmarks (Khalak and Williamson [1999] and Assi et al. [2013, 2010]) with frequency lock-in within 4% and matching critical spacing trends. (3) The framework with Human-in-the-Loop (HIL) discovers more WIV amplitude response phenomena, and uses a neural network to fit physical laws from data, which is 31% higher than that of polynomial fitting. (4) The framework with multi-agent with virtual-real interaction system executes hundreds of experiments end-to-end, which automatically completes the entire process of scientific research from hypothesis generation, experimental design, experimental execution, data analysis, and manuscript preparation. It greatly liberates human researchers and improves study efficiency, providing new paradigm for the development and research of experimental fluid mechanics.

Haodong Feng, Yue Wang, Dixia Fan

In science and engineering, machine learning techniques are increasingly successful in physical systems modeling (predicting future states of physical systems). Effectively integrating PDE loss as a constraint of system transition can improve the model's prediction by overcoming generalization issues due to data scarcity, especially when data acquisition is costly. However, in many real-world scenarios, due to sensor limitations, the data we can obtain is often only partial observation, making the calculation of PDE loss seem to be infeasible, as the PDE loss heavily relies on high-resolution states. We carefully study this problem and propose a novel framework named Re-enable PDE Loss under Partial Observation (RPLPO). The key idea is that although enabling PDE loss to constrain system transition solely is infeasible, we can re-enable PDE loss by reconstructing the learnable high-resolution state and constraining system transition simultaneously. Specifically, RPLPO combines an encoding module for reconstructing learnable high-resolution states with a transition module for predicting future states. The two modules are jointly trained by data and PDE loss. We conduct experiments in various physical systems to demonstrate that RPLPO has significant improvement in generalization, even when observation is sparse, irregular, noisy, and PDE is inaccurate.

Haodong Feng, Peiyan Hu, Yue Wang et al.

Control in fluid environments is an important research area with numerous applications across various domains, including underwater robotics, aerospace engineering, and biomedical systems. However, in practice, control methods often face challenges due to sparse or missing observations, stemming from sensor limitations and faults. These issues result in observations that are not only sparse but also inconsistent in their number and modalities (e.g., velocity and pressure sensors). In this work, we propose a Physics-Informed Representation (PIR) algorithm for multi-modal policies of control to leverage the sparse and random observations in complex fluid environments. PIR integrates sparse observational data with the Partial Differential Equation (PDE) information to distill a unified representation of fluid systems. The main idea is that PDE solutions are determined by three elements: the equation, initial conditions, and boundary conditions. Given the equation, we only need to learn the representation of the initial and boundary conditions, which define a trajectory of a specific fluid system. Specifically, it leverages PDE loss to fit the neural network and data loss calculated on the observations with random quantities and multi-modalities to propagate the information with initial and boundary conditions into the representations. The representations are the learnable parameters or the output of the encoder. In the experiments, the PIR illustrates the superior consistency with the features of the ground truth compared with baselines, even when there are missing modalities. Furthermore, PIR combined with Reinforcement Learning has been successfully applied in control tasks where the robot leverages the learned state by PIR faster and more accurately, passing through the complex vortex street from a random starting location to reach a random target.