Journal of Bionic Engineering
ISSN 1672-6529
CN 22-1355/TB
Editor-in-Chief : Luquan Ren Published by Science Press and Springer
Online Journal
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15 October 2026, Volume 23 Issue 5
Passively Adaptive Robotic Hands: A Trade-off-driven Review of Core Mechanisms, Performance Indicators, and Application Scenarios Journal of Bionic Engineering. 2026, 23 (5): 2645-2672. DOI: 10.1007/s42235-026-00972-0
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Passively adaptive robotic hands have attracted growing attention because they shift part of the burden of grasp adaptation from sensing and control to mechanical design. However, existing reviews often discuss variable stiffness, underactuation, structural deformation, and related strategies separately, making it difficult to compare how different passive mechanisms balance adaptability, load capacity, grasp precision, and control simplicity. This paper provides a trade-off-driven and application-oriented review of passively adaptive robotic hands. The field is synthesized from a mechanism-performanceapplication perspective, covering four major categories: variable-stiffness mechanisms, underactuated coupling and transmission mechanisms, structural deformation mechanisms, and mode-switching and hybrid actuation strategies. These mechanisms are discussed in relation to key performance indicators, including shape adaptability, payload, positional tolerance, impact resistance, lightweight design, and reliability, as well as their relevance to representative scenarios such as daily object grasping, high-load manipulation, and clinical assistive applications. Rather than maximizing any single performance metric, passive adaptive mechanisms primarily contribute by redistributing competing design constraints through mechanical intelligence. Finally, this paper highlights current challenges, discusses limitations in cross-study performance comparison, and outlines promising directions for future research.Related Articles | Metrics
Progress and Perspectives on Biomimetic Design of Human Load Regulation Mechanisms for Passive Lower-limb Exoskeletons: A Design Outlook for Continuous Metamorphic Biomimetic Mechanisms Journal of Bionic Engineering. 2026, 23 (5): 2673-2701. DOI: 10.1007/s42235-026-00962-2
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Passive Lower-Limb Exoskeletons (PLLEs) have emerged as a frontier in the fields of assistive locomotion and rehabilitation robotics due to their significant advantages in biomechanical compatibility, energy efficiency, and system lightweight design. This paper systematically classifies and reviews the research progress on PLLEs over recent decades, focusing on the mechanical power transmission mechanisms and system architectures for locomotion-load assistance. By utilizing a bio-inspired evaluation framework based on human lower-limb load regulation mechanisms, the study addresses the limitations of exoskeleton assistance performance. It highlights the significant impact of human–machine locomotion coupling effects on stress distribution in lower limb joints and the collaboration between humans and exoskeletons, which hinders their application in rehabilitation and prevention. The study proposes an integrated continuous metamorphic mechanism in a biomimetic design to enhance human–machine cooperation of PLLEs by achieving passive compliant dynamic responses aligned with lower limb biomechanics. Two potential research directions are then suggested: I. Bio-kinematic dimensional synthesis of PLLEs considering wearable uncertainties for workspace dexterity and accommodation pre-metamorphosis; II. Bio-dimensional synthesis based on PLLEs' rigid-flexible coupled dynamics for axial impact buffering control during metamorphic process of lower limbs.Related Articles | Metrics
Recent Advances in Biomimetic Joint Lubricants: From Single-function Lubrication and Multifunctional Therapy to Cross-scale Mechanistic Insights Journal of Bionic Engineering. 2026, 23 (5): 2702-2742. DOI: 10.1007/s42235-026-00944-4
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Osteoarthritis (OA) is a common degenerative joint disease. Insufficient joint lubrication in OA patients leads to joint pain, stiffness, and restricted normal physiological activity; therefore, restoring joint lubrication is a key strategy for OA treatment. This review summarizes recent advances in single-function and multifunctional lubricants from three aspects: structure, function, and research methodologies. Single-function lubricants primarily rely on hydration lubrication mechanisms to reduce the coefficient of friction and achieve joint lubrication and wear reduction. However, because they focus solely on interfacial lubrication performance and exhibit limited functionality, they are insufficient to halt the complex pathological progression of OA. This limitation has driven the emergence of multifunctional lubricant systems incorporating anti-inflammatory, antioxidant, tissue repair, and regenerative functions, as well as intelligent stimulus-responsive capabilities. In addition, this review highlights the synergistic roles of multiscale interfacial characterization techniques and molecular dynamics simulations in elucidating both biological and biomimetic lubrication mechanisms. The emerging applications of artificial intelligence and machine learning in lubrication performance prediction, inverse molecular design, and multiscale data integration are also discussed. Finally, key translational barriers are analyzed, including the heavy reliance on idealized model systems and the lack of standardized evaluation criteria. This review aims to provide a scientific foundation and new perspectives for the development of biomimetic joint lubricants and the clinical treatment of osteoarthritis.Related Articles | Metrics
Mechanisms Underlying the High Strength and Toughness of Bamboo: From Biological Architecture to Biomimetic Potential Journal of Bionic Engineering. 2026, 23 (5): 2743-2755. DOI: 10.1007/s42235-026-00958-y
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Bamboo, a natural biomass material with a unique gradient structure and excellent mechanical properties, has received increasing attention owing to its high strength, toughness, and efficient utilization potential. This review systematically summarizes recent advances in the mechanisms and applications of the high strength and toughness of bamboo to elucidate the underlying principles in mechanics and materials science. First, the biological mechanisms responsible for the high strength and toughness of bamboo are examined from three aspects: multiphase composite structure, multilevel hierarchical organization, and multilevel structural optimization. Second, the environmental mechanisms are summarized from two perspectives: the effects of moisture on tissue structure and the influence of temperature on chemical composition. Finally, future research and development directions are outlined, particularly regarding the mechanisms underlying high strength and toughness, advanced material development, and practical applications. This systematic review provides detailed insights into the toughening and strengthening mechanisms of bamboo as a natural composite material. These findings provide a theoretical basis for the design of high-performance biomimetic materials and the high-value utilization of bamboo.Related Articles | Metrics
Superhydrophilic Gradient Surfaces for Directional Droplet Transport and Enhanced Fog Harvesting Journal of Bionic Engineering. 2026, 23 (5): 2756-2762. DOI: 10.1007/s42235-026-00948-0
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Fog collection offers a promising route to mitigating global water scarcity, particularly in arid and coastal regions, yet its practical efficiency is often limited by sluggish droplet capture and transport. Developing surfaces that enable rapid, directional droplet motion while retaining long-term stability and self-cleaning capability remains a critical challenge. Here, inspired by cactus spines and spider silk, we report a Superhydrophilic Gradient Surfaces (SHLGS) fabricated via a simple and scalable combination of 3D printing and spray coating. The wave-like spindle architecture extends the three-phase contact line, enhancing droplet capture and retention, while the superhydrophilic gradient drives spontaneous, directional droplet transport. Energy released during droplet coalescence and deformation further accelerates droplet motion, continuously refreshes the surface, and markedly improves collection efficiency. Consequently, the SHLGS achieves a fog collection rate of up to 18 g cm-2 h-1, together with excellent structural stability and robust self-cleaning performance under prolonged operation. This work establishes a scalable, bio-inspired surface design strategy for efficient fog harvesting and directional liquid transport, with broad implications for water-harvesting and functional surface engineering.Related Articles | Metrics
Liquid-solid Interfacial Friction Modulation for Robust Omniphobic Surface#br# Journal of Bionic Engineering. 2026, 23 (5): 2763-2774. DOI: 10.1007/s42235-026-00967-x
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Omniphobic Liquid-Like Surfaces (OLSs) with fast removal of small droplets are highly desired for applications like heat exchangers and water collection. While OLSs have been widely reported, systematic optimization of fabrication parameters, guided by solid-liquid interfacial friction analysis, to achieve durable OLSs with superior performance remains limited. Here, we systematically investigated the dependence of Lateral Adhesion Force (FLA) on the type and length of flexible polymer chains, plasma Activation Time (tact), and Silanization Time (tsil). Based on these results, the optimal design parameters were identified, yielding an OLS with an ultra-low Sliding Angle (SA) of 3.6° and a FLA of 15.3 μN for a 20 μL water droplet. This enhanced performance is attributed to the optimal matching between the size of the tethered polymer brushes and the spacing between neighboring grafting sites, which enables droplet motion with negligible liquid penetration. Furthermore, Polydimethylsiloxane (PDMS) chains with different molecular lengths exhibit distinct interfacial sliding dynamics: short chains are insufficient to effectively support droplets, whereas excessively long chains tend to form terminal clusters that hinder chain mobility. The optimized OLS demonstrated excellent water repellency towards various water-based liquids and superior optical transparency. Durability tests further confirmed its robust stability under UV irradiation, high temperature, and corrosive environments. Overall, these findings provide fundamental insights into interfacial friction control and rational design of covalently grafted polymer brushes for industrial and biomedical applications.Related Articles | Metrics
Bioinspired Quadrupedal Rock-Climbing Robot with Heterogeneous Fore–Hind Grippers and Knee Parallel Elastic Actuators Journal of Bionic Engineering. 2026, 23 (5): 2775-2800. DOI: 10.1007/s42235-026-00963-1
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Robot rock climbing on natural terrain requires large and well-directed attachment forces on irregular surfaces, utilizing limited onboard energy. This paper presents the Multimodal Adaptive Rock-Climbing Robot Version 2 (MARCBot V2), a human-inspired quadrupedal climber with heterogeneous spiny grippers and minimalist knee Parallel Elastic Actuators (PEAs). The forelimb gripper uses underactuated fingers, Linearly Constrained Compliant Spines (LCCSs), and passive compliance. This design better aligns attachment-force directions with climbing loads, increasing tolerance to local surface geometry. The rubber-padded support mode enables walking on level ground. The hindlimb gripper utilizes a lightweight toe–heel layout, enabling toe-hook/heel-hook support to better resist slip and pitching during transitions and pitch changes. We designed a rubber-cord PEA using a Neo–Hookean model and multi-objective optimization. The PEA effectively reduces peak motor power and mitigates knee joint overload without adding complex mechanisms. Basalt tests report mean shear/normal forces of 62.2/25.9 N (maximum 76.2/31.3 N) for the forelimb. System demos demonstrate transitions from 0 to 70° and vertical climbing. PEA tests reveal a mean power reduction from 48.74 to 45.18 W (estimated 7.3% reduction in cost of transport).Related Articles | Metrics
Untethered Bionic Earthworm-like Robot Based on Yoshimura-Ori Soft Structure and Continuous Peristaltic Wave Gait Journal of Bionic Engineering. 2026, 23 (5): 2801-2822. DOI: 10.1007/s42235-026-00940-8
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Earthworm-inspired soft robots hold promise for navigating complex environments, yet they are often constrained by actuator performance, biomimetic locomotion, and untethered operation. In this study, we present an untethered bionic earthworm-like robot based on Yoshimura-ori soft structure and continuous peristaltic wave gait. Firstly, two segment configurations derived from the Yoshimura-ori structure are proposed: the annular chamber configuration and the central chamber configuration, achieving excellent expansion rates of 54.32% and 78.07%, respectively. Secondly, a comparative analysis of discrete versus continuous peristaltic wave gaits is conducted on robots with these two configuration. The results reveal that the continuous peristaltic wave gait yields higher locomotion velocity than the discrete gait. Under the continuous peristaltic wave gait, the robot with the central chamber configuration exhibits outstanding performance, with a planar locomotion velocity of 12.63 mm/s and a pipeline locomotion velocity of 9.05 mm/s. Finally, a modular untethered robot prototype is constructed, and locomotion experiments confirm that the untethered robot also maintains excellent motion performance. Moreover, the untethered robot successfully traverses varied terrains, demonstrating its outstanding environmental adaptability, feasibility and practical potential.Related Articles | Metrics
An Experimental Method for Dynamic Modeling of Hover-capable Tailless Flapping-wing Micro Air Vehicles Journal of Bionic Engineering. 2026, 23 (5): 2823-2838. DOI: 10.1007/s42235-026-00957-z
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Despite the exceptional maneuverability of hover-capable tailless flapping-wing micro air vehicles, the inherent complexity of their unsteady aerodynamics poses significant challenges for developing precise dynamic models for controller design. To address this, this paper proposes ground-based damping pendulum experiments to construct a full damping dynamic model that incorporates parasitic drag damping. The parasitic drag damping is decoupled from flapping-induced damping by experimentally measuring the damping coefficients across three configurations: with wings and flapping, with wings and no flapping, and without wings. Quantitative analysis reveals that, compared with a model that considers only flapping-induced damping, the full damping dynamic model predicts the oscillation periods of longitudinal and lateral unstable modes decrease by 4.27% and 2.24%, respectively. The accuracy of the full damping model is validated by cascaded PID closed-loop control simulations; compared to flight test data, the root-mean-square errors for pitch and roll attitudes are only 1.78° and 2.78°, respectively. Furthermore, this study investigates the influence of wing geometry on aerodynamic derivatives. Results indicate that flapping-induced damping effects increase as the aspect ratio decreases. Finally, an experimentally corrected aerodynamic derivative estimation method is established. This study provides a feasible empirical modeling framework for the conceptual design and controller synthesis of FWMAVs.Related Articles | Metrics
Bioinspired Ultrafast Underwater Grippers Journal of Bionic Engineering. 2026, 23 (5): 2839-2852. DOI: 10.1007/s42235-026-00959-x
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Waterwheel plant Aldrovanda vesiculosa is found to achieve trap closure in 20–100 ms underwater, which is ten times faster than that of the terrestrial plant Venus flytrap. Although a lot of bioinspired underwater grippers have been developed for rapid actuation, these devices are still limited by their closure responses (typically>180 ms), which is considerably slower than that of the aquatic plant. Herein we proposed and demonstrated a new mechanism for Aldrovanda’s rapid closure through morphological observation, theoretical modeling, and numerical simulation. Inspired by this mechanism, we presented a centimeter-scale biomimetic underwater gripper, which achieves fast underwater closure in 70 ms—approaching the plant’s natural speed. A buckling dynamics model was additionally proposed for the high-precision prediction and control of the gripper’s core actuation. This new design principle would contribute to developing high-performance rapid underwater actuation systems.Related Articles | Metrics
Thrust Performance and Propulsive Efficiency of Bioinspired Piston-Type Synthetic Jet Underwater Propellers Journal of Bionic Engineering. 2026, 23 (5): 2853-2866. DOI: 10.1007/s42235-026-00939-1
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The piston-type synthetic jet propeller represents an emerging underwater propulsion technology, for which enhancing thrust output for the actuator is currently critical challenges. To address these issues, drawing biomimetic inspiration from cephalopods such as the octopus, this paper presents a piston-type synthetic jet propeller actuated by a crank-connecting rod mechanism. An efficiency expression for the propeller is defined by analyzing the force transfer relationship between the piston and the jet, tailored to specific excitation sources and application scenarios. Using numerical simulations, the effects of driving signals and actuator geometric parameters on thrust performance and efficiency are investigated, along with their underlying mechanisms. The results show that when stroke A≥0.02 m, the efficiency curve as a function of frequency f exhibits an extremum. A further increase in A causes this extremum to occur earlier. The crank-connecting rod ratio influences the continuous distribution characteristics of thrust over one cycle: although increasing this parameter enhances thrust, it also reduces efficiency. Both increasing the orifice depth and reducing the orifice diameter help improve the axial proportion of jet velocity, thereby increasing thrust. However, an excessively small orifice diameter restricts the actuator’s ability to exchange fluid with the external environment, leading to a decline in both thrust and efficiency. Further analysis demonstrates that the thrust of the proposed piston-driven propeller exceeds that of the piezoelectric-driven counterpart by 1–2 orders of magnitude. Moreover, under equivalent negative peak thrust conditions, its positive peak thrust reaches 2.12 to 2.35 times that of propellers using the same actuation type.Related Articles | Metrics
Modelling of Turning with Given Radius for Robotic Fish Collaboratively Driven by Pectoral and Caudal Fins Journal of Bionic Engineering. 2026, 23 (5): 2867-2879. DOI: 10.1007/s42235-026-00949-z
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The coordinated turning mechanisms of the pectoral and caudal fins, as well as methods for dynamic modeling, still require further exploration to meet the need for flexible maneuverability of robotic fish in complex environments. The aim of this work is to reveal the turning mechanism of a robotic fish with coordinated pectoral and caudal fins and to establish a dynamic model for its turning motion. We studied the turning motion of a bionic fish within a given radius under the coordinated propulsion of its pectoral and caudal fins. First, a kinematic model of the coordinated propulsion of the pectoral and caudal fins was established. Three turning motion parameters were selected: phase lag and frequency lag of the pectoral fins, and body bending offset. Computational fluid dynamics numerical simulation was then employed to reveal the swimming mechanism during coordinated pectoral-caudal fin turning. Meanwhile, numerical simulation datasets were obtained for different turning parameters. Finally, based on the obtained dataset, a radial basis function neural network was employed to construct a turning dynamics model for the robotic fish, correlating the three turning metrics with its average turning speed, time, and angular velocity. By solving the inverse dynamics model, parameter values for turning motion under target radius and turning time were obtained, enabling the robotic fish to execute turning maneuvers at specified radii. To validate the model’s reliability, experiments were conducted using an independently developed robotic fish. Results showed a 5% error between experimental data and model predictions, confirming the accuracy and reliability of the established turning model. This study provides theoretical reference for turning maneuvers in robotic fish driven by coordinated pectoral fin and caudal fin movements.Related Articles | Metrics
Neural Lyapunov-Guided Reinforcement Learning with LIPM Foothold Convergence for Stable Bipedal Locomotion Journal of Bionic Engineering. 2026, 23 (5): 2880-2895. DOI: 10.1007/s42235-026-00966-y
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This paper proposes a Reinforcement Learning framework for bipedal robots that integrates Lyapunov stability principles with gait prediction based on the Linear Inverted Pendulum Model (LIPM). Unlike conventional approaches that rigidly enforce the policy to track model-planned footholds, the proposed method emphasizes the convergence trend whereby actual footholds gradually approach the desired ones. To achieve this, a neural Lyapunov critic is constructed to incorporate LIPM-predicted footholds and their errors as inputs, learning energy-decreasing patterns to softly constrain policy behavior. Furthermore, a Lyapunov-augmented advantage estimation mechanism is developed, enabling the policy to benefit from both task rewards and stability compensation, thereby unifying physical interpretability, stability guarantees, and the flexibility of Reinforcement Learning. This study conducts large-scale experiments in Isaac Gym with 4096 parallel environments and further validate the approach on the TRON1A bipedal robot. Results demonstrate that the proposed method achieves superior performance in terrain adaptability, velocity tracking capability, stair-climbing success rate, and highly dynamic locomotion tasks. Moreover, the approach exhibits strong sim-to-real transferability, confirming its robustness and generalization in diverse real-world environments.Related Articles | Metrics
A Novel Command Fusion Strategy for Human–robot Collaborative Control of Bionic Hexapod Robot Based on Autonomous Decision-making Model and Finite State Machine Switching Journal of Bionic Engineering. 2026, 23 (5): 2896-2917. DOI: 10.1007/s42235-026-00950-6
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The operational load on operators, imposed by the complex structural characteristics of hexapod robots, leads to muscle fatigue and operational errors during long-duration teleoperation across irregular terrains. Existing autonomous decisionmaking methods for robots are insufficient to meet the demands for high precision and real-time performance. To address these challenges, this paper proposes a remote human–robot collaborative control method for hexapod robots. First, the relationship between terrain features and control commands is analyzed, and a deep learning-based model is constructed to generate autonomous walking commands for the robot in various terrains. Next, a human–robot command allocation method based on state machine switching is designed to optimize command authority allocation and dynamically adjust command combinations, thereby reducing errors. Furthermore, a command fusion method based on human–robot decision reliability is proposed. By evaluating the reliability of decisions made by the operator and the robot system in real time, this method dynamically adjusts the level of human–robot collaboration, thereby improving control accuracy and stability. Finally, human-in-the-loop driving experiments are conducted to validate the effectiveness of the proposed method in complex environments. The experimental results demonstrate that the proposed method significantly enhances the robot’s control precision and motion stability.Related Articles | Metrics
Nonlinear Dynamic Analysis of a Novel Multi-coupled Quadrupedal Bio-inspired Vibration Isolation Platform Journal of Bionic Engineering. 2026, 23 (5): 2918-2934. DOI: 10.1007/s42235-026-00973-z
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In order to achieve ultra-low and broadband frequency vibration suppression, a structurally compact and parameter-adaptable Multi-coupled Quadrupedal Bio-inspired Vibration Isolation platform (MQBVI) based on the mechanical features of the quadruped is proposed in this research. Due to the large working stroke and strong nonlinearity of the platform, the virtual work method and incremental harmonic balance method are utilized to systematically analyze the static and dynamic characteristics, respectively. The comparison validations of bio-inspired platform are conducted by Incremental Harmonic Balance Method (IHBM), ADAMS, numerical method and physical prototype. The investigation revealed that the restoring force and equivalent stiffness are nonlinear and asymmetrical, which lead to the MQBVI platform exhibits superior High Static Low Dynamic Stiffness (HSLDS) characteristics and strong stability. The vibration suppression performance of the MQBVI structure is investigated with installation angle, spring stiffness, connecting rod length, isolated mass and excitation amplitude, which exhibits low resonance frequency and wide effective vibration attenuation frequency band. Notably, the minimum critical values of resonance frequency and vibration suppression effect are reduced to 0.27 Hz and 0.39 Hz with α=30°, respectively. Overall, the proposed MQBVI platform is an efficient ultra-low frequency vibration suppression structure with excellent adaptability, and the bio-inspired vibration buffering and isolation mechanism are revealed.Related Articles | Metrics
Agile Motion Control of Quadruped Robots on Unstructured Terrain Based on 3D Composite Perception and Depth Camera Characteristic Modeling Journal of Bionic Engineering. 2026, 23 (5): 2935-2948. DOI: 10.1007/s42235-026-00941-7
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Quadruped robots have inherent advantages in unstructured terrain, but agile motion control remains challenging. These challenges include insufficient 3D terrain perception and a significant visual domain shift between simulation and reality. Moreover, integrating diverse motion skills remains difficult. This paper proposes an end-to-end motion policy framework to address these issues by integrating precise 3D perception and sensor characteristic modeling. A 3D composite scanning mechanism with three vertical layers and one horizontal layer is designed. It efficiently perceives 3D structures such as overhanging obstacles, without relying on elevation maps or world models. Six types of physical noise from depth cameras are systematically modeled. With simulated image degradation and real-world data homogenization, the distribution of real depth images is accurately reproduced. Based on the teacher-student framework and Dataset Aggregation (DAgger) knowledge distillation, diverse motion skills and zero-shot transfer are integrated end-to-end. Experiments show that the framework enables quadruped robots to climb vertical obstacles, cross gaps, crawl under obstacles, and move stably on sloped grasslands.Related Articles | Metrics
A Bio-inspired Integrated Framework for Disturbance Rejection Whole-Body Control of Humanoid Robots Journal of Bionic Engineering. 2026, 23 (5): 2949-2970. DOI: 10.1007/s42235-026-00965-z
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The dynamic balancing capability of humanoid robots in unstructured terrain and under external force disturbances constitutes a critical challenge for their practical application. This paper proposes an integrated framework combining disturbance estimation, online motion planning, and whole-body control to enhance the robustness of humanoid robots against external disturbances and their adaptability to complex terrains. Firstly, a disturbance observer based on the velocity residual of the Divergent Component of Motion (DCM) is designed. It enables real-time estimation of external force disturbances acting on the robot’s Center of Mass (CoM) without requiring foot force sensors and demonstrates enhanced robustness against model errors and sensor noise. Next, a hierarchical online locomotion planner is proposed: a footstep planner optimizes foot placement positions and gait cycles in real-time using Quadratic Programming (QP), while a gait generator employs a 3D DCM-based Model Predictive Controller (MPC) to generate robust CoM trajectory and gaits based on the planned foot placements. Then, a Disturbance Rejection Whole-Body Controller (DR-WBC) is developed, which incorporates the estimated disturbances into the whole-body dynamics constraints, achieving active disturbance compensation and direct joint torque control. Finally, simulations and experiments conducted on the humanoid robot Dexbot from Harbin Institute of Technology (HIT) demonstrate that the proposed framework effectively enhances the robot’s stable walking capability under disturbances and on uneven terrain, validating its effectiveness and engineering practicality.Related Articles | Metrics
Facial Expression Analysis, Drive Control Design, and Imitation Reproduction for Humanoid Robots Journal of Bionic Engineering. 2026, 23 (5): 2971-2984. DOI: 10.1007/s42235-026-00964-0
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Humanoid robots with realistic facial expression capabilities hold significant potential in medical therapy, education, and the arts by replicating human emotions, thereby enhancing adaptive Human–Robot Interaction (HRI). This work presents a systematic framework for developing a facial system for humanoid robots. Our contributions are fourfold: First, a data-driven method for facial skin drive point selection using the Cohn-Kanade dataset, analyzing landmark displacement patterns to differentiate static and dynamic facial regions. Second, a modular biomimetic facial system integrating six region-optimized actuation units (eyebrows, jaw, eyelids, nasal alar, eyes, mouth corners) with a total of 14 servo motors, a 3D-printed head-shell with static-dynamic partitioning, and anthropomorphic silicone skin fabricated using custom molds. Third, an expression imitation algorithm using 11 morphological geometric features and a neural inverse model (Multilayer Neural Network, MNN) trained on 3000 automatically collected servo-image pairs. Fourth, experimental validation demonstrating accurate expression replication through custom metrics (Mean Error Percentage of Command, MEPC; Mean Error Percentage of Discretization Command, MEPDC) and expression similarity quantification. Our system achieves MEPC of 0.107 and MEPDC of 0.114, outperforming Linear regression, Random Forest, and Support Vector Regression (SVR) models. This work establishes a foundational approach for developing expressive humanoid robot facial systems, enabling emotionally intelligent HRI.Related Articles | Metrics
Adaptive Observation State Selection for a Quadruped Robot Under Varying Task Commands Journal of Bionic Engineering. 2026, 23 (5): 2985-3000. DOI: 10.1007/s42235-026-00954-2
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Reinforcement-learning-based controllers for lightweight robot control in structured, rather than complex, scenarios have received comparatively little attention. Lightweight control aims to achieve performance comparable to full observationbased control by relying on a minimal set of key observation factors. This study finds that different key observation factors become important under different commands. Therefore, the effectiveness of such methods still requires further enhancement. To better understand the influence of observation states on action generation and enhance lightweight control performance, this paper proposes a method based on an improved Integrated Gradients algorithm to quantify the importance of observation variables in quadruped robot control. By combining sampling and fitting techniques, the variation pattern of observation importance weights is derived with respect to different velocity commands, and the optimal observation subsets are identified under specific command conditions. To enable real-time switching of observation subsets during inference based on command input, a multi-encoder training framework is introduced. This framework encodes and learns multiple observation subsets using a shared replay buffer and a Multi-stage Encoder Switching Architecture. Simulation results demonstrate that different observation subsets are optimal for different command ranges. The proposed command-driven observation selection strategy improves the overall performance score by 5.33% compared with fixed Determined State Observation configurations. Real-world experiments validate similar trends, highlighting the potential of this approach for lightweight robot control and the exploration of biologically inspired locomotion mechanisms.Related Articles | Metrics
Research on the Selection and Rapid Positioning of Facial Drive Points for Humanoid Robot Heads by Characterizing Human Facial Expressions Journal of Bionic Engineering. 2026, 23 (5): 3001-3019. DOI: 10.1007/s42235-026-00969-9
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Achieving realistic facial expressions is a central goal in humanoid robot head research. Current methods for determining facial drive points, often based on FACS and design experience, are subjective and prone to bias. This study proposes a quantitative method for selecting facial drive point positions based on optical motion capture and interpolation reconstruction, providing a set of 3D coordinates. On this basis, we further propose a rapid positioning method for robotic drive points applicable to diverse human bionic subjects. Motion data of 238 reflective markers were captured from volunteers performing six basic and one arbitrary facial expression to represent facial movement characteristics. Drive areas were defined based on facial muscle distribution and movement patterns, and the maximum displacement point in each area was calculated using TPS interpolation and displacement field reconstruction to obtain full-face drive point coordinates. For diverse human bionic subjects, proportional correspondences between their inherent facial features and the drive point parameters established in this study were calculated, and new facial drive points were positioned through scaling. To validate the approach, based on the results, a 19-degree-of-freedom humanoid head prototype was built, realizing six basic expressions with recognition rates exceeding 90%, thereby validating the feasibility of the proposed drive point determination method for practical applications. In summary, the proposed methods provide a quantitative reference for subsequent research, enhance design efficiency, and provides a theoretical foundation for achieving more natural and realistic robotic facial expressions.Related Articles | Metrics
A Cross‑Scale Bioinspired Friction‑differential Stepping Positioning Platform Driven by Piezoelectric Bimorph Benders Journal of Bionic Engineering. 2026, 23 (5): 3020-3036. DOI: 10.1007/s42235-026-00946-2
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While piezoelectric positioning platforms show significant potential in micro/nano actuation, their widespread adoption is often limited by inherent structural complexity. To address this, we proposed a cross-scale friction-differential stepping platform driven by only two piezoelectric bimorph benders. Utilizing a specially designed T-shaped structure, the platform achieved both linear and rotational motion through an innovative friction-differential principle. Following theoretical and dynamic simulation analyses, a prototype was fabricated. Experimental results demonstrate stable performance and high repeatability. For linear motion, the resolution was 2.853 μm; at 150 V (no load), the maximum speed reached 3.306 mm/s (30 Hz), with a return deviation of 348.718 μm (1 Hz). For rotational motion, the resolution was 0.063 mrad; the peak angular velocity attained 136.551 mrad/s (15 Hz), with a return deviation of 7.598 mrad. Furthermore, the platform exhibited a maximum payload-to-weight ratio of 63.49. This design offers a simple, redundancy-free 2-DOF solution, significantly reducing structural complexity compared to traditional platforms.Related Articles | Metrics
Bio-inspired CPG Control with Genetic Algorithm-optimized Multi-modal Serpentine Locomotion in Unstructured Terrains Journal of Bionic Engineering. 2026, 23 (5): 3037-3054. DOI: 10.1007/s42235-026-00936-4
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Inspired by the exceptional locomotive efficiency and adaptability of snakes across diverse terrains, this study presents a bio-inspired control framework for snake robots that integrates a Central Pattern Generator (CPG) based on the Matsuoka oscillator with Genetic Algorithm (GA)-optimized parameters to achieve adaptive multi-modal locomotion in unstructured terrains. Inspired by snakes’ exceptional terrain adaptability, the proposed CPG architecture generates rhythmic undulatory motions and enables seamless transitions between serpentine, rectilinear, and concertina gaits through dynamic parameter modulation. Leveraging the Matsuoka oscillator’s inherent stability and nonlinear dynamics, the system adapts to environmental variations while maintaining rhythmic output. Key innovations include the application of GA for optimizing critical parameters, which reduced motion cycle duration by 25%, improved convergence speed by 150%, and minimized steadystate amplitude fluctuations by 40% compared to baseline models. Experimental validation demonstrated the robot’s ability to navigate cluttered environments and inclined surfaces while carrying payloads, supported by its modular elastic-wheel design. This work pioneers a synergistic approach combining biologically inspired control with evolutionary optimization, offering a scalable framework for adaptive robotics. The results highlight significant advancements in gait versatility, energy efficiency, and terrain adaptability, with broad implications for search-and-rescue, environmental monitoring, and industrial inspection applications.Related Articles | Metrics
Biomechanical Effects of Compression Leggings: 3D Finite Element Analysis of Pressure, Tissue Deformation, and Muscle Stress Journal of Bionic Engineering. 2026, 23 (5): 3055-3071. DOI: 10.1007/s42235-026-00968-w
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Compression leggings act as external bio-functional supports that enhance postural stability and gait performance. This study developed a subject-specific three-dimensional Finite Element (FE) model of the female lower body to investigate the biomechanical interactions between compression leggings and underlying tissues, focusing on interface pressure, soft tissue deformation, and intramuscular stress. A distinctive and comprehensive methodology reconstructed anatomically accurate geometries from high-resolution Magnetic Resonance Imaging data to segment nine major muscle groups. Region-specific hyperelastic properties were assigned from in vivo indentation tests, and orthotropic fabric properties were characterised through uniaxial tension and shear testing. FE simulations revealed non-uniform responses: interface pressure decreased from the calf to the low hip before increasing at the high hip, with higher anterior pressures linked to anatomical curvature. Tissue deformation peaked at the high hip and was minimal at the calf, while muscle stress reflected tissue stiffness and pressure, with the highest values in the calf anterior. These findings inform biomechanics-oriented design strategies, where gradient compression and fabrics with varied elasticity, anisotropic stretch, or engineered knits are optimised to align with local tissue properties and curvature. Model predictions agreed with experimental measurements (errors: 15.4% in pressure; 16.0% in deformation), supporting digital evaluation and virtual optimisation of compression leggings to enhance functionality, comfort, and realism in both physical and metaverse applications.Related Articles | Metrics
Implementation of Football Tactile Monitoring Using Cuttlefish Cartilage-based β-chitin Triboelectric Array Journal of Bionic Engineering. 2026, 23 (5): 3072-3090. DOI: 10.1007/s42235-026-00937-3
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Friction electric nanogenerators based on natural biomaterials have become a research hotspot in sports tactile monitoring since their self-powering ability, biocompatibility, and flexibility. To design a green, flexible, and high-performance tactile sensor device, this study innovatively used a lithium chloride/N-methylpyrrolidone solvent system to extract β-chitin from discarded squid cartilage. A composite nanofiber membrane was constructed using electrospinning method, and a cuttlefish cartilage-based β-chitin triboelectric array was successfully prepared. The experiment demonstrated that the peak output voltage of the frictional electric array at 3 Hz frequency was 117.0 V. After 5,000 cycles, the peak voltage remained at about 116.8 V, and the waveform shape was basically the same as the initial stage, with a peak decrease of less than 1.0%. Further placement of the frictional electric array at the heel of the football insole successfully monitored changes in foot pressure under different motion states. The output currents under walking, running, and sprinting conditions were 3.2 μA, 5.4 μA, and 8.6 μA, with stable signals and high discrimination. This study demonstrates the potential application of natural β-chitin materials in flexible self-powered sensors and provides a high-sensitivity, low-cost tactile monitoring solution for intelligent training in football.Related Articles | Metrics
Precise Inner Ear Delivery of Injectable GelMA Hydrogel Containing Andrographolide Promotes Repair of Diabetic Hearing Loss Journal of Bionic Engineering. 2026, 23 (5): 3091-3109. DOI: 10.1007/s42235-026-00953-3
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Given the poor efficacy of conventional oral medications in treating inner ear disorders due to the presence of the BloodLabyrinth Barrier (BLB) in the inner ear, we designed an inner ear injectable Andro@GelMA hydrogel for the repair of Diabetic Hearing Loss (DHL). Natural protein-derived materials, such as collagen and gelatin, hold broad prospects in tissue engineering and regenerative medicine. Specifically, Gelatin Methacryloyl Acetate (GelMA), a photosensitive polymer obtained by modifying gelatin with methacrylic anhydride, inherits the high biocompatibility of collagen, making it an ideal drug delivery carrier. In this study, FTIR, XRD, SEM, and rheological tests demonstrated that hydrogen-bonding linkages formed between Andrographolide (Andro) and GelMA, thereby enhancing cross-linking degree and structural stability. Additionally, in vitro and in vivo tests confirmed that the Andro@GelMA hydrogel could achieve controllable sustained release by adjusting the cross-linking degree. Furthermore, in vitro cellular experiments showed strong protective effects on auditory cells, while animal experiments verified that this local delivery system significantly improved the therapeutic efficacy of DHL and promoted the regeneration of damaged inner ear hair cells compared to the control group.Related Articles | Metrics
QLOA: A Self-Adaptive Q-Learning-Based Optimization Algorithm with Dynamic Mathematical Formulation Selection Journal of Bionic Engineering. 2026, 23 (5): 3110-3178. DOI: 10.1007/s42235-026-00961-3
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In the field of optimization, one of the fundamental challenges of existing methods lies in their inability to dynamically adapt to the diverse characteristics of objective functions. Many algorithms rely on a fixed optimization strategy; therefore, while they may perform well on certain problems, they often lose efficiency when dealing with functions exhibiting different behaviors, such as smooth or steep landscapes. To overcome this limitation, this study introduces a smart and self-adaptive approach called the Q-Learning-Based Optimization Algorithm (QLOA). The proposed QLOA incorporates a set of diverse mathematical formulations designed to enhance both the exploration and exploitation phases. A key feature of QLOA lies in the integration of the Q-learning framework, which enables the algorithm to intelligently and adaptively select the most suitable formulation based on the problem characteristics and its performance feedback, thereby establishing a dynamic balance between exploration and exploitation at each stage of the optimization process. In addition, population refinement mechanisms—such as eliminating redundant members and applying structural adjustments—prevent the algorithm from becoming trapped in local optima. To further enhance adaptability in problems with hard and soft constraints, an extended version named QLOA with Constraint Management (QLOA-CM) is developed. Experimental results on standard benchmark functions and the CEC2019 and CEC2022 test suites demonstrate that QLOA outperforms reference algorithms in both the Friedman and Wilcoxon statistical tests, confirming its efficiency, robustness, and statistically significant superiority over existing methods. Final evaluations of QLOA-CM on engineering optimization problems and real-world challenges from CEC2020, alongside QLOA’s successful application in image segmentation tasks, further validate the effectiveness and generalization capabilities of the proposed approaches in solving complex optimization problems. The source code of the proposed algorithm is publicly available at https://github.com/MSNFV/QLOA-Q-Lear ning-based-Optimization-Algorithm.Related Articles | Metrics
Neural Perception Optimization Algorithm: A Novel Meta-heuristic Algorithm Inspired by the Cooperative Optimization Mechanism of the Nervous System for Global Optimization Journal of Bionic Engineering. 2026, 23 (5): 3179-3212. DOI: 10.1007/s42235-026-00952-4
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Inspired by the hierarchical coordination mechanism of the nervous system, this paper proposes a multi-layer co-evolutionary Neural Perception Optimization Algorithm (NPOA) for complex optimization problems. The proposed algorithm is built upon three core modules. First, we design a gated elite layer inspired by the prefrontal cortex that integrates dualsource attention and spatial gating to guide the search toward high-value regions and regulate search directions. Second, inspired by hippocampal associative learning, we develop a differential association-based synaptic development layer for the structured reuse of historical search information and refined local search. Finally, to mimic the stimulus-response mechanism of the sensory cortex, we introduce a stimulus exploration layer with probabilistic switching updates to preserve diversity and balance exploration and exploitation. Through the information interaction and coordinated functioning among these modules, NPOA constructs a unified search framework that enhances population collaboration, improves information reuse, and strengthens global-local coordination throughout the evolutionary process. To assess its performance, NPOA was evaluated against more than ten advanced metaheuristic algorithms on benchmark functions and practical constrained optimization problems. Experimental results showed that NPOA achieved competitive or superior performance in terms of solution accuracy, convergence speed, and robustness, demonstrating its effectiveness and potential for solving complex optimization problems. Source code is available at the link in the end of this paper.Related Articles | Metrics
MRAF-Net: A Multi-stage Recursive Alignment and Fusion Network for High-precision 3D Medical Image Registration Journal of Bionic Engineering. 2026, 23 (5): 3213-3235. DOI: 10.1007/s42235-026-00943-5
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Non-rigid 3D medical image registration, which establishes dense anatomical correspondences between scans, is a critical step in clinical diagnosis and surgical planning. However, existing methods struggle to address three key challenges simultaneously: capturing complex anatomical deformations, balancing global alignment with local detail preservation, and maintaining computational efficiency.To overcome these limitations, we introduce MRAF-Net, a Multi-stage Recursive Alignment and Fusion network designed for high-precision registration with minimal computational overhead. MRAFNet adopts a multi-stage encoder-decoder scheme. It begins with a Hierarchical Residual Encoder (HR-Encoder), which incorporates a Hybrid Anti-Aliasing Downsampling (HAAD) to extract multi-scale features while preserving structural integrity and suppressing aliasing artifacts during downsampling. Within the decoder, the core Progressive Alignment Module (PAM) recursively propagates and refines deformation fields across scales. The PAM integrates a Context-Aware Feature Fusion Module (CAFM) to model spatial-channel correspondences between images, and a lightweight Spatial Residual Flow Head (SRFH) for parameter-efficient local deformation prediction. Experiments on LPBA40, OASIS, and IXI datasets demonstrate that MRAF-Net generates anatomically plausible deformation fields with superior topological integrity. Comprehensive evaluations against the strong baseline TransMorph reveal that MRAF-Net achieves a 6.7% higher Dice score (DSC), reduces the 95% Hausdorff Distance (HD95) by 38.1%, and lowers the Average Symmetric Surface Distance (ASSD) by 41.9% on the LPBA40 dataset, while requiring 60% fewer parameters (18.7 M vs 46.5 M). These results confirm the method's efficiency and accuracy for high-resolution clinical deployment.Related Articles | Metrics
Dynamic Spectral Calibration Integrated with Diffusion Based Temporal Fusion for Accurate and Interpretable Hyperspectral Brain Tumor Segmentation Journal of Bionic Engineering. 2026, 23 (5): 3236-3262. DOI: 10.1007/s42235-026-00955-1
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The segmentation of brain tumors, based on hyperspectral imaging (HSI), has been attracting considerable interest for its capability of providing detailed spectral–spatial information about tissue. Current segmentation methods based on HSI have limitations such as spectral noise, illumination changes, high dimensionality of data, and temporal variation between successive surgical frames, which can impact the accuracy of segmentation and its clinical utility. In this work, we suggest a dynamic spectral calibration (DSC) integrated with diffusion-based temporal fusion (DTF) framework to overcome these limitations and achieve interpretable and low latency brain tumor segmentation in HSI. It is based on a spectral-attentive denoising stage using a deep convolutional autoencoder to remove spectral noise while maintaining the most important biochemical and morphological tissue properties. Then, a diffusion-assisted spectral–spatial tumor mapping module is used to iteratively refine the tumor boundary using a reverse diffusion method. A DSC module adaptively recalibrates the spectral responses based on a gradient guided spectral prior optimization to increase robustness in varying illumination conditions during surgery. Moreover, the Hierarchical Spatial–Temporal Integration module integrates multiscale spatial representations and temporal feature learning via recurrent attention mechanisms and gated recurrent units to ensure temporal coherence between successive frames. The explainable artificial intelligence module is also integrated to offer interpretable visualization of spectral and spatial decision patterns, offering clinical transparency and confidence in the model predictions. Experimental results on hyperspectral brain tumor datasets show that the proposed DSC–DTF framework provides competitive segmentation results with dice similarity coefficient of 97.12%, intersection over union of 94.47%, sensitivity of 96.32%, specificity of 97.18%, Hausdorff distance of 3.42 mm, spectral angle mapper of 3.41° and Temporal Consistency Index of 95.25%. The outcomes demonstrate the effectiveness of the proposed framework in enhancing the spectral consistency, segmentation accuracy, and temporal stability of the hyperspectral brain tumor data while maintaining its interpretability and computational efficiency for real-time intraoperative support in analyzing brain tumors.Related Articles | Metrics
A Novel Cervical Cancer Cell Classification using Convolutional Jacobian Kolmogorov Arnold Network model Journal of Bionic Engineering. 2026, 23 (5): 3263-3281. DOI: 10.1007/s42235-026-00942-6
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Cervical cancer is a primary cause of death in women throughout the world, and early identification using cell classification is essential for increasing survival rates. Timely and accurate detection of cancer cells is critical for promoting personalized treatment and clinical diagnostics. This paper introduces Conv-Jacobian Kolmogorov Arnold Network (ConvJKAN), a novel deep-learning architecture specifically designed for high-accuracy cervical cancer cell classification from cytological images. The Conv-JKAN uniquely integrates convolutional neural networks with the Jacobian Kolmogorov Arnold network, enabling enhanced feature extraction while maintaining computational efficiency. The model employs just three convolutional layers and three JKAN layers to capture intricate spatial and contextual patterns across varying resolutions, ensuring superior recognition of subtle cytopathological changes. The novelty of Conv-JKAN lies in its hierarchical decomposition approach, where JKAN dissects high-dimensional functions into low-dimensional components using Jacobian polynomial-based sensitivity analysis. This novel technique enhances both interpretability and gradient flow, addressing common challenges in deep-learning-based medical diagnostics. To validate its robustness, Conv-JKAN was rigorously tested on three public cytology datasets, achieving high classification performance: 100%, 99.75%, and 96.52% accuracy in binary classification, and 99.7%, 98.73%, and 96.35% in multi-class classification on the Mendeley LBC, SIPaKMeD, and Herlev datasets, respectively. Furthermore, we integrated explainable artificial intelligence (XAI) techniques within Conv-JKAN to provide transparent and interpretable insights into the model’s decision-making, which is crucial for real-world clinical adoption.Related Articles | Metrics
EAL-Net: Evolutionary Algorithm-optimized Novel Lightweight Deep Learning Architecture with Multi-attention Modules and Orthogonal Softmax for Blood Cell Diagnosis Journal of Bionic Engineering. 2026, 23 (5): 3282-3311. DOI: 10.1007/s42235-026-00956-0
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Traditional diagnostic methods for Blood Cells (BCs) and Cervical Cells tend to erroneous analysis and inaccurate diagnoses due to the complexity involved in overlapping regions of cells. Deep Learning (DL) techniques through Convolutional Neural Networks (CNNs) have gained prominence in addressing these issues but encounter challenges as inefficient feature attention, and high computational processing power. To tackle these inefficiencies, this paper presents a novel computationally efficient lightweight architecture (EAL-Net) for BCs diagnosis, which is based on lightweight multi-attention modules and Orthogonal SoftMax Layer (OSL). OSL functionality precisely mitigates parameter co-adaptation to ensure orthogonality among weight vectors, thus refining feature learning processes. The developed EAL-Net architecture is equipped with novel Lightweight Attention Mechanism (LWAM) to selectively learn discriminative features and enabling more precise attention on diagnostic relevant regions. LWAM integrates Spatial-Attention Module (SAM) to focus on key regions, Spatial Self-Attention Module (SSAM) to capture long-range dependencies, and Category-Attention Module (CAM) to emphasize class-specific features. Collectively, this approach amplifies feature attention and strengthening spatial and channel-wise dependencies, significantly improving the performance of neural network architecture. Moreover, Genetic Algorithms (GA) efficiently search the optimal set of hyperparameters iteratively. GA is chosen for its efficacy in handling complex search spaces and non-linear optimization problems. Additionally, Grad-CAM and SHAP provide model insights by highlighting key features influencing predictions. EAL-Net outperforms pre-trained CNNs, transformer-based architectures, and existing methods across accuracy, efficiency, and memory use. With only 0.73 million parameters and 8.2 MB size, it achieves 96.11% accuracy on 8-class and 93.68% on 19-class BCs datasets. To validate the robustness of the proposed architecture across diverse medical imaging modalities, we evaluated EAL-Net on Cervical Cells (SIPaKMeD & Mendeley_LBC), histopathological and chest X-ray datasets.Related Articles | Metrics
Hybrid Deep Learning Framework for Systemic Lupus Erythematosus Detection Using Xception Convolutional Neural Network with Black-winged Frigate Optimization Journal of Bionic Engineering. 2026, 23 (5): 3312-3334. DOI: 10.1007/s42235-026-00947-1
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Systemic Lupus Erythematosus (SLE) is a long-term autoimmune disease where the immune system mistakenly targets and damages healthy tissues and organs. Prevailing models delayed the diagnosis and failed to detect the disease in its early stages, which led to worse patient outcomes and less effective treatments. Therefore, the Xception Convolutional Neural Network with Black-Winged Frigate Optimization Algorithm (XCovNet_Bla-WFOA) is developed for effective SLE detection. First, the input data is collected from the database, and then data normalization is done by Z-score normalization. Besides, relevant features are selected by the proposed Black-Winged Frigate Optimization Algorithm (BlaWFOA), which fuses the strengths of Magnificent Frigatebird Optimization (MFO) and Black-Winged Kite Algorithm (BKA). Next, data augmentation is accomplished by the Synthetic Minority Over-sampling Technique (SMOTE). Consequently, Lupus Erythematosus detection is implemented by Xception Convolutional Neural Network (XCovNet), where the newly established Bla-WFOA is exploited for optimizing the XCovNet to enhance the detection process. Finally, the Explainable Artificial Intelligence-SHapley Additive exPlanations (XAI-SHAP) are utilized to interpret the detected results. The XCovNet_Bla-WFOA model obtained an accuracy of 93.877%, sensitivity of 95.776%, and specificity of 92.988% for K-value 8.Related Articles | Metrics
Artificial Neural Network Simulation of Radiative Hybrid Nanofluid Flow with Forchheimer Resistance on a Permeable Sheet Journal of Bionic Engineering. 2026, 23 (5): 3335-3361. DOI: 10.1007/s42235-026-00960-4
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This study presents a numerical simulation utilizing the Levenberg–Marquardt backpropagation (LMBP) algorithm to examine the radiative flow of hybridized cobalt ferrite (CoF e2O4) and magnetite (Fe3O4) nanofluids over a permeable stretching surface, with a focus on the Forchheimer effect. Hybrid nanofluids, which consist of nanoparticles with distinct thermophysical properties, are known to exhibit enhanced heat transfer performance compared to conventional single-phase fluids. The incorporation of radiation heat transfer and the Forchheimer effect into the fluid model offers a more comprehensive representation of complex heat transport processes relevant to industrial applications. A novel hybrid nanofluid composed of cobalt ferrite and magnetite nanoparticles is introduced, demonstrating a significant improvement in the thermal characteristics of the base fluid. A similarity transformation was applied to convert the governing partial differential equations into ordinary differential equations (ODEs). The impacts of various parameters on the flow field were investigated and visualized through graphical plots. Numerical solutions obtained via the BVP4C (boundary value problem 4C) method was compared with existing literature, showing excellent agreement. The findings contribute to the optimization of thermal management systems in advanced engineering and industrial processes. Additionally, the LMBP algorithm was validated through error analysis, regression metrics, adaptive control parameter evaluations, and iterative learning curve studies, demonstrating convergence, accuracy, and efficiency. Performance verification was conducted using regression plots, mean squared error (MSE), and error histograms, ensuring the robustness of the LMBP approach in solving the problem. In addition, the numerical solution is obtained by training the network with the LMPB algorithm by developing an accurate surrogate using 70%/10%/10% split for training/testing/validation. The LMPB algorithm obtained a best MSE of 4 · 04419 × 10-9 at epoch 890, with errors closely grouped around zero and an overall regression coefficient R ～ = 1 across the process demonstrating excellent agreement with the numerical targets.Related Articles | Metrics
