arXiv subjects

Dixia Fan

Publications and source records attributed to Dixia Fan.

At least 19 recordsLinked to original sources

arXiv2026

Turbulence Physics Governs a Scaling Law for the Machine-Learning Predictability Ceiling in Chaotic Flow

For centuries, the intrinsic chaos of unsteady fluid motion has stood as a formidable barrier to long-term forecasting. While machine learning (ML) has recently emerged as a transformative paradigm for predicting flow evolution, it encounters a pervasive yet unexplained "performance wall": an inevitable deterioration in accuracy as the forecast horizon extends. Here, we demonstrate that this deterioration is not a deficiency of model architecture, no matter how state-of-the-art, but a fundamental constraint imposed by the underlying system, which can be understood through turbulence theory established decades ago. In the setting of bluff body flow, a canonical phenomenon for spatiotemporal complexity in fluid mechanics, we reveal a scaling law governing the deterioration of ML predictability, derived from a Kolmogorov-inspired framework and validated through high-fidelity simulations. Our findings establish a closed loop between the predictability ceiling and its interpretation, bridging the gap between transparent physical theories and modern black-box inference. More broadly, this work provides a theoretical compass for constructing trustworthy ML in complex dynamical systems across the physical sciences.

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arXiv2026

Swimming Under Constraints: A Safe Reinforcement Learning Framework for Quadrupedal Bio-Inspired Propulsion

Bio-inspired aquatic propulsion offers high thrust and maneuverability but is prone to destabilizing forces such as lift fluctuations, which are further amplified by six-degree-of-freedom (6-DoF) fluid coupling. We formulate quadrupedal swimming as a constrained optimization problem that maximizes forward thrust while minimizing destabilizing fluctuations. Our proposed framework, Accelerated Constrained Proximal Policy Optimization with a PID-regulated Lagrange multiplier (ACPPO-PID), enforces constraints with a PID-regulated Lagrange multiplier, accelerates learning via conditional asymmetric clipping, and stabilizes updates through cycle-wise geometric aggregation. Initialized with imitation learning and refined through on-hardware towing-tank experiments, ACPPO-PID produces control policies that transfer effectively to quadrupedal free-swimming trials. Results demonstrate improved thrust efficiency, reduced destabilizing forces, and faster convergence compared with state-of-the-art baselines, underscoring the importance of constraint-aware safe RL for robust and generalizable bio-inspired locomotion in complex fluid environments.

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arXiv2026

RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data

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/.

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arXiv2025

Towards an AI Fluid Scientist: LLM-Powered Scientific Discovery in Experimental Fluid Mechanics

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.

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arXiv2025

UnderwaterVLA: Dual-brain Vision-Language-Action architecture for Autonomous Underwater Navigation

This paper presents UnderwaterVLA, a novel framework for autonomous underwater navigation that integrates multimodal foundation models with embodied intelligence systems. Underwater operations remain difficult due to hydrodynamic disturbances, limited communication bandwidth, and degraded sensing in turbid waters. To address these challenges, we introduce three innovations. First, a dual-brain architecture decouples high-level mission reasoning from low-level reactive control, enabling robust operation under communication and computational constraints. Second, we apply Vision-Language-Action(VLA) models to underwater robotics for the first time, incorporating structured chain-of-thought reasoning for interpretable decision-making. Third, a hydrodynamics-informed Model Predictive Control(MPC) scheme compensates for fluid effects in real time without costly task-specific training. Experimental results in field tests show that UnderwaterVLA reduces navigation errors in degraded visual conditions while maintaining higher task completion by 19% to 27% over baseline. By minimizing reliance on underwater-specific training data and improving adaptability across environments, UnderwaterVLA provides a scalable and cost-effective path toward the next generation of intelligent AUVs.

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arXiv2025

LinguaFluid: Language Guided Fluid Control via Semantic Rewards in Reinforcement Learning

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.

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arXiv2025

Vortex-Induced Drag Forecast for Cylinder in Non-uniform Inflow

In this letter, a physics-based data-driven strategy is developed to predict vortex-induced drag on a circular cylinder under non-uniform inflow conditions - a prevalent issue for engineering applications at moderate Reynolds numbers. Traditional pressure-signal-based models exhibit limitations due to complex vortex dynamics coupled with non-uniform inflow. To address this issue, a modified fully connected neural network (FCNN) architecture is established that integrates upstream velocity measurements (serving as an inflow calibration) with pressure-signal-based inputs to enhance predictive capability (R^2 ~ 0 to 0.75). Direct numerical simulations (DNS) at Reynolds number Re = 4000 are implemented for model training and validation. Iterative optimizations are conducted to derive optimized input configurations of pressure sensor placements and velocity components at upstream locations. The optimized model achieves an R^2 score of 0.75 in forecasting high-amplitude drag coefficient fluctuations (C_d=0.2 - 1.2) within a future time window of one time unit. An exponential scaling between model performance and optimized pressure signal inputs is observed, and the predictive capability of sparsely distributed but optimized sensors is interpreted by the scaling. The optimized sensor placements correspond to the physical mechanism that the flow separation dynamics play a governing role in vortex-induced drag generation. This work advances machine learning applications in fluid-structure interaction systems, offering a scalable strategy for forecasting statistics in turbulent flows under real-world engineering conditions.

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arXiv2025

Physics-Informed Neural Networks for the Korteweg-de Vries Equation for Internal Solitary Wave Problem: Forward Simulation and Inverse Parameter Estimation

Physics-informed neural networks (PINNs) have emerged as a transformative framework for addressing operator learning and inverse problems involving the Korteweg-de Vries (KdV) equation for internal solitary waves. By integrating physical constraints with data-driven optimization, PINNs overcome the critical challenges of parameter unmeasurability in the KdV equation for internal solitary waves in two-layer fluid systems. This work addresses two problems: (1) Operator learning constructs a mapping from parameters to solutions, enabling wave evolution predictions from unknown parameters. Comparative studies demonstrate prediction errors as low as $10^{-4}$ when using 1000 training points. (2) Inverse problem solving leverages sparse and potentially noisy observational data with physics-regularized constraints to invert nonlinear coefficients successfully. Compared to conventional approaches, this end-to-end differentiable paradigm unifies operator learning and inverse problem-solving while overcoming mesh discretization errors and high-dimensional parameter space iteration costs. The method shows effectiveness for internal wave problems in stratified fluids, providing both accurate forward modeling and robust parameter inversion capabilities, even under noise.

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arXiv2025

Enhancing Efficiency and Propulsion in Bio-mimetic Robotic Fish through End-to-End Deep Reinforcement Learning

Aquatic organisms are known for their ability to generate efficient propulsion with low energy expenditure. While existing research has sought to leverage bio-inspired structures to reduce energy costs in underwater robotics, the crucial role of control policies in enhancing efficiency has often been overlooked. In this study, we optimize the motion of a bio-mimetic robotic fish using deep reinforcement learning (DRL) to maximize propulsion efficiency and minimize energy consumption. Our novel DRL approach incorporates extended pressure perception, a transformer model processing sequences of observations, and a policy transfer scheme. Notably, significantly improved training stability and speed within our approach allow for end-to-end training of the robotic fish. This enables agiler responses to hydrodynamic environments and possesses greater optimization potential compared to pre-defined motion pattern controls. Our experiments are conducted on a serially connected rigid robotic fish in a free stream with a Reynolds number of 6000 using computational fluid dynamics (CFD) simulations. The DRL-trained policies yield impressive results, demonstrating both high efficiency and propulsion. The policies also showcase the agent's embodiment, skillfully utilizing its body structure and engaging with surrounding fluid dynamics, as revealed through flow analysis. This study provides valuable insights into the bio-mimetic underwater robots optimization through DRL training, capitalizing on their structural advantages, and ultimately contributing to more efficient underwater propulsion systems.

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arXiv2025

SpineWave: Harnessing Fish Rigid-Flexible Spinal Kinematics for Enhancing Biomimetic Robotic Locomotion

Fish have endured millions of years of evolution, and their distinct rigid-flexible body structures offer inspiration for overcoming challenges in underwater robotics, such as limited mobility, high energy consumption, and adaptability. This paper introduces SpineWave, a biomimetic robotic fish featuring a fish-spine-like rigid-flexible transition structure. The structure integrates expandable fishbone-like ribs and adjustable magnets, mimicking the stretch and recoil of fish muscles to balance rigidity and flexibility. In addition, we employed an evolutionary algorithm to optimize the hydrodynamics of the robot, achieving significant improvements in swimming performance. Real-world tests demonstrated robustness and potential for environmental monitoring, underwater exploration, and industrial inspection. These tests established SpineWave as a transformative platform for aquatic robotics.

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arXiv2025

Learn to Swim: Data-Driven LSTM Hydrodynamic Model for Quadruped Robot Gait Optimization

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.

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arXiv2024

AeroDiT: Diffusion Transformers for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows

Real-time and accurate prediction of aerodynamic flow fields around airfoils is crucial for flow control and aerodynamic optimization. However, achieving this remains challenging due to the high computational costs and the non-linear nature of flow physics. Traditional Computational Fluid Dynamics (CFD) methods face limitations in balancing computational efficiency and accuracy, hindering their application in real-time scenarios. To address these challenges, this study presents AeroDiT, a novel surrogate model that integrates scalable diffusion models with transformer architectures to address these challenges. Trained on Reynolds-Averaged Navier-Stokes (RANS) simulation data for high Reynolds-number airfoil flows, AeroDiT accurately captures complex flow patterns while enabling real-time predictions. The model demonstrates impressive performance, with mean relative $L_2$ errors of 0.1, 0.025, and 0.050 for pressure $p$ and velocity components $u_x, u_y$, confirming its reliability. To further enhance physical consistency, we incorporate explicit physics-informed losses based on RANS residuals, including mass and momentum conservation constraints. The transformer-based structure allows for real-time predictions within seconds, enabling efficient aerodynamic simulations. This work underscores the potential of generative machine learning techniques to advance computational fluid dynamics, offering potential solutions to challenges in simulating high-fidelity aerodynamic flows.

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arXiv2024

How to Re-enable PDE Loss for Physical Systems Modeling Under Partial Observation

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.

cs.LG↗

arXiv2024

LE-PDE++: Mamba for accelerating PDEs Simulations

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.

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arXiv2024

Multi-modal Policies with Physics-informed Representations in Complex Fluid Environments

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.

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arXiv2024

DamFormer: Generalizing Morphologies in Dam Break Simulations Using Transformer Model

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.

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arXiv2024

Learning Adaptive Hydrodynamic Models Using Neural ODEs in Complex Conditions

Reinforcement learning-based quadruped robots excel across various terrains but still lack the ability to swim in water due to the complex underwater environment. This paper presents the development and evaluation of a data-driven hydrodynamic model for amphibious quadruped robots, aiming to enhance their adaptive capabilities in complex and dynamic underwater environments. The proposed model leverages Neural Ordinary Differential Equations (ODEs) combined with attention mechanisms to accurately process and interpret real-time sensor data. The model enables the quadruped robots to understand and predict complex environmental patterns, facilitating robust decision-making strategies. We harness real-time sensor data, capturing various environmental and internal state parameters to train and evaluate our model. A significant focus of our evaluation involves testing the quadruped robot's performance across different hydrodynamic conditions and assessing its capabilities at varying speeds and fluid dynamic conditions. The outcomes suggest that the model can effectively learn and adapt to varying conditions, enabling the prediction of force states and enhancing autonomous robotic behaviors in various practical scenarios.

cs.RO↗

arXiv2024

M$^{2}$M: Learning controllable Multi of experts and multi-scale operators are the Partial Differential Equations need

Learning the evolutionary dynamics of Partial Differential Equations (PDEs) is critical in understanding dynamic systems, yet current methods insufficiently learn their representations. This is largely due to the multi-scale nature of the solution, where certain regions exhibit rapid oscillations while others evolve more slowly. This paper introduces a framework of multi-scale and multi-expert (M$^2$M) neural operators designed to simulate and learn PDEs efficiently. We employ a divide-and-conquer strategy to train a multi-expert gated network for the dynamic router policy. Our method incorporates a controllable prior gating mechanism that determines the selection rights of experts, enhancing the model's efficiency. To optimize the learning process, we have implemented a PI (Proportional, Integral) control strategy to adjust the allocation rules precisely. This universal controllable approach allows the model to achieve greater accuracy. We test our approach on benchmark 2D Navier-Stokes equations and provide a custom multi-scale dataset. M$^2$M can achieve higher simulation accuracy and offer improved interpretability compared to baseline methods.

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