Tao Li

Undulatory propulsion is widely employed by biological and engineered swimmers across multiple scales, from fish and bioinspired underwater robots to flagellar, ciliary, and field-driven micro/nanoswimmers. Despite substantial progress in experiments, numerical simulations, theory, and robotic implementation, existing studies remain fragmented across Reynolds-number regimes, propulsion modes, system architectures, and performance metrics, limiting direct comparison and extraction of transferable design principles. To address this gap, this review organizes undulatory propulsion within a cross-scale, mechanism-centered framework following the common sequence of actuation, realized deformation, fluid interaction, and functional performance. Particular emphasis is placed on how structural and material mechanics transform biological, electromechanical, or field-based actuation into spatiotemporal deformation and how this deformation generates propulsion through regime-dependent fluid physics. For inertia-influenced swimmers, the roles of body and fin kinematics, flexibility, fluid–structure interaction, vortex dynamics, neuromuscular regulation, robotic actuation, sensing, and adaptive control are synthesized. For low-Reynolds-number systems, flagellar and ciliary transport, synchronization, complex-fluid effects, and externally driven micro/nanoswimmers are reviewed, with attention paid to viscous anisotropy, non-reciprocal deformation, elastoviscous coupling, and remote field control. Environmental effects, collective interactions, maneuverability, and practical deployment constraints are also discussed. The analysis shows that cross-scale similarity lies primarily in the organization of actuation, deformation, and feedback, whereas the dominant force-generation mechanisms and control architectures remain strongly scale and regime dependent. This framework provides a comparative basis for identifying transferable principles, regime-specific constraints, and design strategies for efficient, maneuverable, and adaptable bioinspired propulsion systems.

In biomimetic underwater systems, high-efficiency and low-power propulsion remains a core challenge. Mimicking the characteristics of fish caudal fins and exploring highly biomimetic muscle-driven approaches is regarded as one of the key strategies to address this issue.This study combines the immersed boundary-lattice Boltzmann (IB-LB) method with deep reinforcement learning (DRL) to investigate the interactive effects of caudal fin structural stiffness and active muscle control on propulsive performance and energy consumption.By constructing a virtual fish model with a closed-loop ``perception--decision--action'' feature, the agent can autonomously learn to output tail torque based on environmental feedback, thereby regulating the deflection behavior of the caudal fin. The research evaluates the differences in dynamic responses between rigid and flexible caudal fin configurations under both passive states and active control intervention. The results indicate that rigid caudal fins exhibit significant phase lag and increased energy consumption without control; however, driven by DRL strategies, they can achieve phase compensation and a substantial improvement in propulsive performance. In contrast, flexible caudal fins, relying on stronger passive adaptability, can achieve superior propulsive efficiency in the uncontrolled state, while their speed and energy consumption can be further optimized with the introduction of active regulation.To realize dynamic trade-offs between speed and energy consumption, this study develops a task-sensitive multi-objective dynamic reward function, enabling the agent to switch between ``high-speed propulsion'' and ``high-efficiency energy-saving'' strategies according to requirements. This research not only reveals the synergistic relationship between structural compliance and active control but also demonstrates the potential of deep reinforcement learning in exploring optimal control strategies without prior knowledge. It provides a new research path and theoretical support for the intelligent regulation of bionic fish caudal fins and the design of flexible underwater robots.

Fundamental research on fluid seepage has become a hot topic in numerous scientific and engineering fields. However, the current understanding of seepage in complex layered porous structures and the influence of temperature on seepage remains incomplete. In this study, to investigate the flow and heat transfer characteristics of subsurface seepage in saturated soils with a multilayer structure, a thermal-flow coupled lattice Boltzmann model was developed by using a multiple relaxation time operator and the Runge–Kutta fourth-order difference scheme. This study investigates the effects of inflow velocity, inflow temperature, and solid substrate size on pore-scale flow and heat transfer within multilayer porous media. Results show that higher inflow velocity increases permeability and enhances heat penetration into colder soil layers, with inertial effects and fluid–solid interactions requiring larger pressure gradients. At constant porosity, larger solid substrate diameters yield higher permeability due to wider pore throats and reduced viscous resistance. Elevated inflow temperatures decrease fluid viscosity, promote pore-scale flow, and accelerate thermal equilibrium. For layered porous media (LPM), changes in porosity lead to variations in the number and structure of internal preferential flow paths, which in turn affect the displacement process of the high-temperature fluid. Besides, based on Pearson's theory and chi-square test, the analysis found that the pore-scale velocity distribution followed a lognormal distribution. The results enhanced the understanding of the coupled mechanisms between seepage and heat transfer in LPM and provided a theoretical basis for engineering applications involving subsurface thermal hydraulic processes.

Path planning is a core issue in fields such as robotics, autonomous driving, and unmanned navigation systems. Nevertheless, traditional path planning methods face substantial challenges in dynamic, nonlinear, and stochastic underwater environments. In this study, a fluid solver module capable of simulating fluid–structure interaction with high precision and efficiency was constructed based on the immersed boundary–lattice Boltzmann method. The perception and decision-making system of the bionic intelligent fish was constructed using deep reinforcement learning (DRL) algorithms, and a concise visual perception modality representation based on one-hot encoding was proposed. The obstacle avoidance performance of the bionic intelligent fish trained via end-to-end DRL was tested in both still-water environments and dynamic flow environments with complex geometries. The results demonstrate that the intelligent fish exhibits efficient local path planning and obstacle avoidance capabilities in both environments while possessing a certain robustness against disturbances in nonlinear environments. This research can provide a reference for the design of local path planning modules for bionic robotic fish and is expected to further enhance the mission execution capabilities of autonomous underwater vehicles in unmapped deep and far-sea areas with high uncertainty.

Fish schooling, an adaptive strategy shaped by long-term evolution, is closely associated with core biological needs such as survival and reproduction. This study, having adopted a numerical simulation framework built by combining the deep reinforcement learning algorithm with the immersed boundary-lattice Boltzmann fluid–solid interaction simulation method, focused on investigating the effects of modal transitions on energy efficiency and array dynamics during large-scale turning of fish schools under low hydrodynamic pressure environments. Initially, strategic control was applied to two fish utilizing body–caudal fin propulsion, aiming to explore their schooling modes and the intrinsic energy-saving mechanisms inherent to each mode. Subsequently, the school size was expanded non-proportionally, and the influence of modal transitions on energy consumption was analyzed through a leader-guided turning strategy. Results indicated that under low hydrodynamic pressure, carangiform fish exhibited three modes in their modal composition, namely, the vortex action mode, the lateral force action mode, and the combined action mode. Additionally, with an increased number of schooling individuals, the modal transitions of carangiform fish demonstrated greater arbitrariness and flexibility. Notably, exclusive reliance on hydrodynamic information perception via the lateral line could enhance efficiency in small-scale schools. However, as the school expanded, the complex flow field limited the ability of this approach to significantly improve overall schooling performance; meanwhile, in low hydrodynamic pressure environments, the collective movement of fish schools does not depend solely on hydrodynamic information. These findings provide theoretical guidance and strategic foundations for the design of clustered bionic underwater intelligent robots with different undulatory propulsion modes.

This study extended a hybrid immersed boundary-lattice Boltzmann method (IB-LBM) to analyze the hydrodynamic and thermodynamic behaviors of a fluid heat exchanger (FHE) with an asymptotic tube configuration. The effects of Reynolds number (Re), superheat levels, porosity, and cylinder arrangements on temperature and flow velocity were primarily examined. Several thermodynamic parameters were introduced as metrics to evaluate the thermal efficiency of the FHE. The results revealed that the Re significantly influenced the hydrodynamic and thermodynamic behaviors of the FHE. Pressure drops increased with higher Re, while the rapid decline in average heat flux was attributed to reduced conductive heat transfer caused by decreasing temperature difference. Moreover, superheat levels directly impacted the outlet temperature but primarily affected the frequency of flow velocity fluctuations. The average flow frequency, determined through the fast Fourier analysis, helps avoid resonance with the structure's natural frequency, thereby preventing potential structural failures. Additionally, five different porosity and cylinder configurations were analyzed to evaluate their impact on thermal performance of the FHE. The findings from this research provide valuable insights for enhancing the thermal efficiency of the FHE.

The design and optimization of fishways and other fish-passage facilities are one of the critical issues in hydraulic engineering. Traditional methods using physical experiments for fishway design and optimization face challenges such as the uncontrollability of fish behavior, limited non-intrusive measurement techniques, and nonlinear scale effects. Numerical simulation methods can provide the hydraulic performance information of fishways by analyzing flow velocity, turbulence energy, and flow patterns, but fail to account for the active responses of fish to the hydrodynamic characteristics of the environment. In this study, a research paradigm of using embodied intelligent fish to optimize eco-hydraulic facilities was attempted. The core of this research paradigm is a simulation platform for intelligent fish based on deep reinforcement learning (DRL) and the immersed boundary–lattice Boltzmann (IB-LB) coupling algorithm. Based on this platform, by endowing fish with biological tendencies and biometric features related to perception/feedback/decision-making at the individual scale, embodied intelligent fish can achieve multimodal perception and autonomous decision-making in complex fishway digital flow fields based on the potential habits of live fish. Using the proposed framework, conduct end-to-end deep reinforcement learning training on intelligent fish and then deploy the trained embodied intelligent fish in a virtual vertical-slot fishway for ecological hydrodynamic experiments. Comparative analyses were conducted on the fish-passage performance of three different fishway geometric shapes. The results demonstrated that the new research paradigm evaluates the structural characteristics of fishways through the adaptive response behavior of fish to the hydrodynamic environment, which can provide quantitative guidance for fishway design from the terms of passage path, passage time, energy consumption, etc. This study belonged to an individual-scale digital twin and was an innovative attempt to utilize virtual intelligent lifeforms at the individual scale to conduct simulation-based experimental research.

The study of fish swimming behaviours and locomotion mechanisms holds significant scientific and engineering value. With the rapid advancements in artificial intelligence, a new method combining deep reinforcement learning (DRL) with computational fluid dynamics has emerged and been applied to simulate the fish’s adaptive swimming behaviour, where the complex fish behaviour is decoupled to focus on the fish’s response to the hydrodynamic field, and the simulation is driven by reward-based objectives to model the fish’s swimming behaviour. However, the scale of this cross-disciplinary method is directly affected by the efficiency of the DRL model. To promote it to more general application scenarios, there is a pressing need for further research on more efficient and economical network architectures to address the challenge of approximating state-value function in high-dimensional, dynamic, and uncertain environments. Building upon a previously proposed computational platform for the simulation of fish autonomous swimming behaviour, we integrated Kolmogorov–Arnold Networks(KANs) and tested their performance in point-to-point swimming and Kármán gait swimming environments. Experimental results demonstrated that, compared to long short-term memory Networks(LSTMs) and multilayer perceptron networks(MLPs), the introduction of KANs significantly enhanced the perception and decision-making abilities of the intelligent fish in complex fluid environments. With a smaller network scale, in the point-to-point swimming case, KANs effectively approximated the state-value function, achieving average reward improvements of up to 88.0% and 94.1% over MLPs and LSTMs networks, respectively, and increased by 766.7% and 105.6% in the Kármán gait swimming case. Under comparable network sizes, the intelligent fish with KANs exhibited faster learning capabilities and more stable swimming performance in complex fluid settings.

The study of fish swimming behavior and locomotion mechanisms holds substantial scientific and engineering significance. With the rapid progression of artificial intelligence, the integration of artificial intelligence with high-precision numerical simulation methods presents a novel and highly efficient tool for investigating fish behavior. In this paper, we proposed a fish perception model that more closely reflects natural logic. By introducing the individual vision and partially visibility model, a physics-based visual system that mirrored the sensory capabilities of live fish was developed. Furthermore, through the construction of a flow vision using conventional neural networks, we enhanced the intelligent fish's ability to detect unsteady hydrodynamic parameters via numerical lateral line. The validity of the new model was demonstrated through experiments, which the intelligent fish hunts complex moving targets in unsteady flow. Finally, we applied the model to study the refuge/predation behaviors of coral reef fish under varying unsteady flow pressures. The results indicated that swimming capabilities significantly impact fish survival strategies in high flow velocity, highly unsteady hydrodynamic environments, shaping distinct evolutionary decision-making traits. These insights may help to understand the niche competition mechanisms of fish in different flow conditions.

The reef ecosystem plays a vital role as a habitat for fish species with limited swimming capabilities, serving not only as a sanctuary and food source but also influencing their behavioral tendencies. Understanding the intricate mechanism through which fish adeptly navigate the moving targets within reef environments within complex water flow, all while evading obstacles and maintaining stable postures, has remained a challenging and prominent subject in the realms of fish behavior, ecology, and biomimetics alike. An integrated simulation framework is used to investigate fish predation problems within intricate environments, combining deep reinforcement learning algorithms (DRL) with high-precision fluid-structure interaction numerical methods-immersed boundary lattice Boltzmann method (lB-LBM). The Soft Actor-Critic (SAC) algorithm is used to improve the intelligent fish’s capacity for random exploration, tackling the multi-objective sparse reward challenge inherent in real-world scenarios. Additionally, a reward shaping method tailored to its action purposes has been developed, capable of capturing outcomes and trend characteristics effectively. The convergence and robustness advantages of the method elucidated in this paper are showcased through two case studies: one addressing fish capturing randomly moving targets in hydrostatic flow field, and the other focusing on fish counter-current foraging in reef environments to capture drifting food. A comprehensive analysis was conducted of the influence and significance of various reward types on the decision-making processes of intelligent fish within intricate environments.