Dixia Fan

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.

Athanasios Oikonomou, Theodoros Loutas, Dixia Fan et al.

Calibration of highly dynamic multi-physics manufacturing processes such as electro-hydrodynamics-based additive manufacturing (AM) technologies (E-jet printing) is still performed by labor-intensive trial-and-error practices. These practices have hindered the broad adoption of these technologies, demanding a new paradigm of self-calibrating E-jet printing machines. To address this need, we developed GPJet, an end-to-end physics-informed Bayesian learning framework, and tested it on a virtual E-jet printing machine with in-process jet monitoring capabilities. GPJet consists of three modules: a) the Machine Vision module, b) the Physics-Based Modeling Module, and c) the Machine Learning (ML) module. We demonstrate that the Machine Vision module can extract high-fidelity jet features in real-time from video data using an automated parallelized computer vision workflow. In addition, we show that the Machine Vision module, combined with the Physics-based modeling module, can act as closed-loop sensory feedback to the Machine Learning module of high- and low-fidelity data. Powered by our data-centric approach, we demonstrate that the online ML planner can actively learn the jet process dynamics using video and physics with minimum experimental cost. GPJet brings us one step closer to realizing the vision of intelligent AM machines that can efficiently search complex process-structure-property landscapes and create optimized material solutions for a wide range of applications at a fraction of the cost and speed.

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.

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/.

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.

Aoming Liang, Chi Cheng, Dashuai Chen et al.

In the domain of scientific machine learning, designing effective reward functions remains a challenge in reinforcement learning (RL), particularly in environments where task goals are difficult to specify numerically. Reward functions in existing work are predominantly based on heuristics, manual engineering, or task-specific tuning. In this work, we introduce a semantically aligned reinforcement learning method where rewards are computed by aligning the current state with a target semantic instruction using a Sentence-Bidirectional Encoder Representations from Transformers (SBERT). Instead of relying on manually defined reward functions, the policy receives feedback based on the reward, which is a cosine similarity between the goal textual description and the statement description in the episode. We evaluated our approach in several environments and showed that semantic reward can guide learning to achieve competitive control behavior, even in the absence of hand-crafted reward functions. Our study demonstrates a correlation between the language embedding space and the conventional Euclidean space. This framework opens new horizons for aligning agent behavior with natural language goals and lays the groundwork for a more seamless integration of larger language models (LLMs) and fluid control applications.

Fei Han, Pengming Guo, Hao Chen et al.

This paper presents a Long Short-Term Memory network-based Fluid Experiment Data-Driven model (FED-LSTM) for predicting unsteady, nonlinear hydrodynamic forces on the underwater quadruped robot we constructed. Trained on experimental data from leg force and body drag tests conducted in both a recirculating water tank and a towing tank, FED-LSTM outperforms traditional Empirical Formulas (EF) commonly used for flow prediction over flat surfaces. The model demonstrates superior accuracy and adaptability in capturing complex fluid dynamics, particularly in straight-line and turning-gait optimizations via the NSGA-II algorithm. FED-LSTM reduces deflection errors during straight-line swimming and improves turn times without increasing the turning radius. Hardware experiments further validate the model's precision and stability over EF. This approach provides a robust framework for enhancing the swimming performance of legged robots, laying the groundwork for future advances in underwater robotic locomotion.

Aoming Liang, Zhaoyang Mu, Qi liu et al.

Partial Differential Equations are foundational in modeling science and natural systems such as fluid dynamics and weather forecasting. The Latent Evolution of PDEs method is designed to address the computational intensity of classical and deep learning-based PDE solvers by proposing a scalable and efficient alternative. To enhance the efficiency and accuracy of LE-PDE, we incorporate the Mamba model, an advanced machine learning model known for its predictive efficiency and robustness in handling complex dynamic systems with a progressive learning strategy. The LE-PDE was tested on several benchmark problems. The method demonstrated a marked reduction in computational time compared to traditional solvers and standalone deep learning models while maintaining high accuracy in predicting system behavior over time. Our method doubles the inference speed compared to the LE-PDE while retaining the same level of parameter efficiency, making it well-suited for scenarios requiring long-term predictions.

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.

Zhaoyang Mul, Aoming Liang, Mingming Ge et al.

The interaction of waves with structural barriers such as dams breaking plays a critical role in flood defense and tsunami disasters. In this work, we explore the dynamic changes in wave surfaces impacting various structural shapes, e.g., circle, triangle, and square, by using deep learning techniques. We introduce the DamFormer, a novel transformer-based model designed to learn and simulate these complex interactions. The model was trained and tested on simulated data representing the three structural forms.

Dixia Fan, Liu Yang, Michael S Triantafyllou et al.

We demonstrate experimentally the feasibility of applying reinforcement learning (RL) in flow control problems by automatically discovering active control strategies without any prior knowledge of the flow physics. We consider the turbulent flow past a circular cylinder with the aim of reducing the cylinder drag force or maximizing the power gain efficiency by properly selecting the rotational speed of two small diameter cylinders, parallel to and located downstream of the larger cylinder. Given properly designed rewards and noise reduction techniques, after tens of towing experiments, the RL agent could discover the optimal control strategy, comparable to the optimal static control. While RL has been found to be effective in recent computer flow simulation studies, this is the first time that its effectiveness is demonstrated experimentally, paving the way for exploring new optimal active flow control strategies in complex fluid mechanics applications.