Search Results (397)

Multimodal multi-objective optimization problems often exhibit one-to-many mappings, where multiple distinct variable vectors correspond to the same objective vector. This characteristic makes Pareto set (PS) estimation difficult, as conventional inverse modeling approaches assume a one-to-one correspondence. This study proposes a cluster-wise PS estimation framework in the variable space. Known solutions are partitioned into locally monotonic clusters using oscillation detection with an amplitude threshold, and independent response surface models are constructed for each cluster. By estimating PS solutions from multiple cluster-specific models for a given direction vector, the method preserves multimodal structures that conventional approaches fail to capture. Numerical experiments on the multimodal benchmark problems MMF1–8 and LIRCMOP1–2 demonstrate that the proposed method achieves equal or better HV and IGD values than the conventional method, while improving decision-space approximation as measured by IGDX in most test cases and suppressing the generation of dominated solutions. Full article

Accurate inverse kinematics for rehabilitation robotic arms remains challenging because of strong nonlinearity, multiple feasible joint configurations, and strict joint-limit constraints. Inspired by the cooperative construction, adaptive exploration, and collective information-sharing behaviors of beavers, this study develops an improved biomimetic beaver behavior optimizer (IBBO) for optimization-based inverse kinematics solving. In the proposed framework, biologically inspired cooperative search is translated into an engineering-oriented numerical strategy through four complementary mechanisms: a strict elitist replacement with rollback to preserve population fitness consistency, a momentum-inspired information transfer scheme to accumulate effective search directions, a lightweight memetic coordinate-wise local search to strengthen late-stage exploitation, and an adaptive builder–disturbance schedule to progressively shift the search from exploration to refinement. The optimization capability of IBBO is first evaluated on the CEC2017 benchmark suite, where it demonstrates competitive accuracy and robustness. It is then applied to inverse kinematics solving for representative rehabilitation robotic arms by minimizing pose errors under joint constraints. The experimental results show that IBBO can consistently generate feasible joint solutions with improved terminal pose accuracy and stable convergence compared with baseline metaheuristics. Beyond numerical improvement, this study provides a biomimetic optimization framework that transfers beaver-inspired cooperative behaviors into rehabilitation robotics, offering an effective computational approach for constrained inverse kinematics problems. Full article

We study one-dimensional diffusions reflected at a boundary and analyze their pathwise “episodes” away from the boundary through Itô’s excursion theory. Under a fixed height cap of $a>0$, each excursion is equipped with three natural marks: its lifetime $\zeta$, its maximum $M$, and an additive (area-type) functional $A_f={\int }_0^{\zeta }f\left(e_t\right)dt$. Our main object is the height-truncated Itô-excursion Laplace exponent ${\mathsf{\Psi }}_{\alpha ,\lambda ;af}:=n\left(1-e^{-\alpha \zeta -\lambda A_f}; M<a\right)$ which jointly characterizes episode duration and cumulative load while excluding barrier-crossing spikes. We establish a general boundary–flux representation: ${\mathsf{\Psi }}_{\alpha ,\lambda ;af}$ is obtained as a boundary flux (in scale) of the unique solution to a one-dimensional killed Feynman–Kac boundary-value problem on $(0, a)$. This transfer principle yields a unified and tractable route to explicit computation. We implement it in three solvable families—the reflected arithmetic Brownian motion, reflected Ornstein–Uhlenbeck diffusions, and squared Bessel/Bessel-type diffusions—obtaining closed forms in terms of Airy, parabolic-cylinder, and confluent hypergeometric/Whittaker functions. Using the Poisson point process structure of excursions indexed by local time, we derive explicit extreme-burst laws (maxima and order statistics) for the additive marks up to a local-time horizon, and connect tail intensities to Laplace exponents via numerical Laplace inversion. Finally, we identify the strictly truncated cumulative load in local time as a (typically infinite-activity) subordinator whose Lévy measure coincides with the excursion-mark intensity, linking cumulative-load and extreme-burst statistics through the same exponent. Full article

This paper studies an inverse problem associated with the time-fractional Schrödinger equation in a field-free potential. To address the severe ill-posedness of the problem, a mollification regularization method with truncated kernels is employed to obtain stable approximate solutions. Both a priori and a posteriori strategies for selecting the regularization parameter are developed, and corresponding error estimates for the regularized solutions are derived. The effectiveness of the proposed approach is demonstrated through numerical simulations. Full article

Structural damage detection using the finite element method is inherently formulated as an inverse problem, often suffering from ill-posedness and high sensitivity to measurement noise. This study introduces a novel damage detection methodology by applying low-rank adaptation (LoRA), originally developed for fine-tuning large language models, to inverse problems in structural mechanics for the first time. The proposed approach exploits the physically inherent low-rank nature of structural damage: damage is typically localized, and the contribution of each finite element to the stiffness matrix is limited by its degrees of freedom. Accordingly, the stiffness change matrix is factorized into two low-rank matrices, reducing the number of parameters and providing implicit regularization against full-rank measurement noise. Physical consistency is ensured through sparsity and symmetry constraints. Numerical experiments on cantilever beam and L-shaped plate structures across five damage scenarios demonstrated that the proposed method achieved superior noise robustness compared with baseline methods. At a signal-to-noise ratio of 20 dB, representative of practical field conditions, LoRA achieved stiffness errors below 2%, whereas the baseline methods failed to provide reliable results. The proposed framework achieved a 100% success rate in damage zone localization (Precision@n ≥ 80%) with over 60% parameter reduction, presenting a promising solution for practical structural health monitoring. Full article

The load transfer method is important for the settlement prediction of axially loaded piles, but in multi-layered complex soils, it lacks analytical solutions. Traditional numerical methods such as the finite element method suffer from strong dependence on mesh generation, time-consuming iterative calculations, and high computational costs for back-analysis. This paper proposes a load transfer analysis model based on a Domain Decomposition Physics-Informed Neural Network. A multi-subnet parallel architecture is adopted to simulate multi-layered soils, solving the problem of inter-layer stress–strain discontinuity through interface coupling and gradient continuity constraints; a non-dimensionalization system and a hard constraint mechanism are introduced to enhance training efficiency and physical consistency; and a two-stage analysis framework comprising surrogate model forward analysis and field data inversion is established. Numerical experimental results indicate that the forward analysis of this model is in high agreement with FEM simulation results, and computational efficiency is improved by six orders of magnitude; based on a small amount of field static load test data, multi-layer soil parameters are accurately inverted, achieving more precise pile settlement prediction than FEM. Comparative analysis validates the effectiveness of the domain decomposition multi-subnet over a single network, demonstrating extensibility to hyperbolic and exponential multi-soil constitutive models. Full article

This work develops numerical methods for the modified Korteweg–de Vries (mKdV) equation based on an inverse-problem formulation that identifies key solution parameters. The resulting inverse problems are treated using a variational approach that reformulates the original ill-posed formulation into an alternative well-posed minimization problem suitable for numerical computation. Numerical experiments with solitary and periodic waves demonstrate the accuracy, stability, and robustness of the proposed methods. In addition, the inverse problem framework introduced here represents a significant contribution of this study, because it provides a new computational approach for obtaining periodic solutions that existing methods cannot capture. Full article

Quantitative evaluation of human motion from image data requires both high geometric precision and mathematical interpretability. To address the limitations of pixel-level posture analysis and empirical performance scoring, this study proposes a geometry-driven quantitative modeling framework for image-based motion evaluation. Sub-pixel edge detection based on quadratic polynomial interpolation is first employed to construct a precise continuous representation of limb contours from image sequences. By abstracting the human arm as a spatial rigid-body system, posture evaluation is reformulated as an optimization problem governed by geometric constraints and physical principles. An optimal swing trajectory is obtained by minimizing the total kinetic energy of the system, which is solved numerically using Newton’s iterative method, avoiding the explicit solution of highly coupled inverse kinematics. To further analyze the contribution of multiple performance-related variables within a unified quantitative framework, a hybrid feature attribution strategy integrating Random Forest, XGBoost, and LightGBM is introduced. The proposed mixed feature mining approach reduces model dependency and enhances the robustness of factor importance ranking. The effectiveness of the proposed framework is validated using image data collected from a cloud-based table tennis classroom. The experimental results demonstrate that the geometry-driven modeling approach provides stable, interpretable, and discriminative evaluation outcomes, indicating its potential applicability to broader image-based human motion analysis tasks. Full article

We calculate the mechanical response $r\left(x,t\right)$ of an initially quiescent semi-infinite homogeneous medium to a pulse applied at the origin, and this is achieved within the framework of the Kelvin–Voigt model. Although this problem has been extensively studied in the literature because of its wide range of applications—particularly in seismology—here, we present a solution in a novel integral form. This integral solution avoids the numerical computation of the solution in terms of the inverse Laplace transform; that is, numerical integration in the complex plane. In particular, we derive integral form expressions for both delta-pulse and step-pulse excitations which are simpler and more computationally efficient than those previously reported in the literature. Furthermore, the obtained expressions allow us to obtain simple asymptotic formulas for $r\left(x,t\right)$ as $x,t\to 0,\infty$ for both step- and delta-type pulses. Full article

Accurate joint estimation of heterogeneous hydraulic conductivity fields and time-varying contaminant source parameters in groundwater systems constitutes a challenging high-dimensional inverse problem, particularly under sparse observational conditions and high computational demands. To alleviate this limitation, this study proposes an autoregressive depthwise convolutional neural network (AR-DWCNN) as a lightweight surrogate model for coupled groundwater flow and contaminant transport simulations. The proposed model employs depthwise separable convolutions and dense connectivity within an encoder–decoder framework to capture nonlinear flow and spatiotemporal transport dynamics while reducing model complexity and computational demand relative to conventional convolutional architectures. The AR-DWCNN is further integrated with an enhanced Iterative Local Updating Ensemble Smoother incorporating Levenberg–Marquardt regularization, enabling efficient joint inversion of high-dimensional hydraulic conductivity fields and multi-period contaminant source strengths. Numerical experiments conducted on a synthetic two-dimensional heterogeneous aquifer demonstrate that the surrogate-assisted inversion framework achieves posterior estimates that closely match those obtained using the numerical forward model, while significantly improving computational efficiency. These results indicate that the AR-DWCNN-based inversion method provides an effective and scalable solution for high-dimensional groundwater contaminant transport inverse problems, offering practical potential for uncertainty quantification and remediation design in complex subsurface systems. Full article

In this study, a three-dimensional Inverse Conjugate Heat Transfer Problem (ICHTP) is numerically and experimentally investigated to estimate the heat-source strength of multiple chips mounted on a printed circuit board (PCB) using the Conjugate Gradient Method (CGM) and infrared thermography. The interfaces between the PCB and the surrounding air domain are assumed to exhibit perfect thermal contact, establishing a fully coupled conjugate heat transfer framework for the inverse analysis. Unlike the conventional Inverse Heat Conduction Problem (IHCP), which typically only accounts for conduction within solid domains, the present ICHTP formulation requires the simultaneous solution of the governing continuity, momentum, and energy equations in the air domain, along with the heat conduction equation in the chips and PCB. This coupling introduces substantial computational complexity due to the nonlinear interaction between convective and conductive heat transfer mechanisms, as well as the sensitivity of the inverse solution to measurement uncertainties. The numerical simulations are conducted first with error-free measurement data and an inlet velocity of u_in = 4 m/s; the recovered heat-sources exhibit excellent agreement with the true values. The computed average errors for the estimated temperatures ERR1 and estimated heat sources ERR2 are as low as 0.0031% and 1.87%, respectively. The accuracy of the estimated heat sources is then experimentally validated under various prescribed inlet air velocities. During experimental verification at an inlet velocity of 4 m/s, the corresponding ERR1 and ERR2 values are obtained as 0.91% and 3.34%, while at 6 m/s, the values are 0.86% and 2.81%, respectively. Compared with the numerical results, the accuracy of the experimental estimations decreases noticeably. This discrepancy arises because the numerical simulations are free from measurement noise, whereas experimental data inherently include uncertainties due to thermal picture resolutions, environmental fluctuations, and other uncontrollable factors. These results highlight the inherent challenges associated with inverse problems and underscore the critical importance of obtaining precise and reliable temperature measurements to ensure accurate heat source estimation. Full article

In the present study, we develop numerical approaches for the simultaneous determination of a time-dependent right-hand side and a Robin boundary coefficient in linear and quasilinear Caputo time-fractional reaction–diffusion problems based on boundary and interior observations. The well-posedness of the corresponding direct problems is established. A temporal semidiscretization is first constructed using the $L2-1_{\sigma }$ scheme, and the solution is decomposed with respect to the unknown functions. The correctness of the proposed method is proved. For the nonlinear diffusion problem, a quasilinearization technique is employed, and the spatial discretization is carried out using finite difference schemes. An iterative procedure is developed to solve the resulting inverse problem. Numerical simulations with noisy data are presented and discussed to demonstrate the efficiency of the method. Full article

This study systematically investigates the kinematic characteristics and static stability of a spatial under-constrained four-cable-driven parallel mechanism, specifically designed for supporting aircraft models in wind tunnel tests. Addressing the inherent strong coupling between kinematics and statics in such systems, an integrated solution framework is proposed. Firstly, a hybrid intelligent algorithm integrating genetic algorithm, chaos optimization, and particle swarm optimization is introduced to efficiently solve the direct and inverse geometric-statics problems, ensuring the identification of physically feasible equilibrium configurations under constraints such as cable tension limits and mechanical interference. Subsequently, a stability evaluation method based on the eigenvalue analysis of the system’s total stiffness matrix is employed, establishing a criterion (minimum eigenvalue λ_min > 0) to identify statically stable equilibrium points. Finally, the static feasible workspace and the static stable workspace are systematically analyzed and quantified, providing practical operational limits for mechanism design and trajectory planning. The effectiveness of the proposed solution framework is validated through numerical computations, simulations, and experimental tests, demonstrating its superiority over benchmark methods. This study provides theoretical support for the design, analysis, and control of under-constrained four-cable-driven parallel mechanisms. Full article

Polymer-assisted hot water flooding (PAHWF) is an important enhanced oil recovery technique involving strongly coupled thermal, chemical, and multiphase flow processes. Accurate prediction of water saturation, polymer concentration, and temperature evolution in PAHWF is challenging due to the highly nonlinear and multiscale governing equations. In this study, a physics-informed neural network (PINN) framework is developed for one-dimensional PAHWF simulation as a controlled benchmark system to systematically investigate PINN behavior in multiphysics-coupled problems. The PAHWF governing equations incorporating temperature- and concentration-dependent viscosity are embedded into the PINN loss function. Three progressively designed numerical examples are conducted to examine the effects of temperature normalization, network architecture (PINN-1 versus PINN-2), and network depth on training stability and solution accuracy. The results demonstrate that temperature normalization effectively mitigates gradient-scale imbalance, significantly improving convergence stability and prediction accuracy. Furthermore, the PINN-2 architecture, which employs a dedicated network for temperature, exhibits enhanced robustness and accuracy compared with the unified PINN-1 structure. Variations in network depth show limited influence on solution quality, indicating the inherent robustness of PINNs under the proposed framework. Although conventional numerical methods remain more efficient for one-dimensional forward problems, this study establishes a methodological foundation for extending PINNs to higher-dimensional, strongly coupled PAHWF simulations and inverse reservoir problems. The proposed framework provides insights into improving PINN trainability and reliability for complex enhanced oil recovery processes. Full article

“Experiments were conducted at DIMEG, University of Calabria, located in the main campus in Arcavacata di Rende, Italy.” This article focuses on the study of the geometry, direct and inverse kinematics, workspace, and singularity of a novel 3-PRRS parallel manipulator (PM) with a redundantly actuated architecture. The PM consists of three active revolute joints and three passive prismatic redundant input joints, all located on a fixed platform. The constant and variable parameters characterizing the PM’s geometry and kinematics are determined. The direct kinematics problem is formulated as a 16th-degree polynomial, while the inverse kinematics problem is solved in closed form. A comparison of the direct and inverse kinematics is provided, and the correctness of the solutions is validated through numerical examples. The equations of motion for the moving platform are derived, and the PM’s workspace is defined based on the inverse kinematics. This work demonstrates how the passive prismatic input joints, specifically included in the design, contribute to an enlarged workspace—particularly in the vertical direction—compared to traditional 3-RRS PM architecture. Full article