Search Results (1,033)

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

Closed-form analytic inverses allow explicit tracking of parameter effects, facilitate interpretation of experimental signals, and support solving inverse problems. Here, we derive a rigorous closed-form expression for the inverse Laplace transform of a class of shifted quasi-rational spectral functions with a square-root radical and a power-law decaying factor. These functions appear in coupled diffusion processes in physics and in the analysis of electromagnetic signal propagation through electrically cascaded networks, signal processing, and related areas. The transform is expressed as a finite sum of three generalized hypergeometric functions—two Kummer functions and one five-parameter Kampé de Fériet function—each multiplied by a monomial depending on the decay parameter. The validity of the result is confirmed by direct Laplace transformation, which recovers the original spectral function. Several known inverse transforms appear as limiting cases, illustrating the generality of the solution. Additionally, reduction formulas for a subclass of Kampé de Fériet functions demonstrate how the general solution encompasses previously known results and highlight the generality of the method. Full article

W. Takahashi and M. Toyoda (2003) proved weak convergence of an iteration process of solving a variational inequality problem for an inverse strongly-monotone mapping. In our recent work we showed that, for the same iterative process, most of its exact iterates are approximate solutions of the variational inequality. In this paper, we show that the iteration process for solving a variational inequality problem for an inverse strongly monotone mapping generates an approximate solution in the presence of small computational errors. We also estimate a number of iterates needed in order to obtain such an approximate solution. Full article

Lanthanide-based single-molecule magnets are promising candidates for potential applications. Their magnetism is governed by ligand-field splittings, which may require up to 27 ligand-field parameters for accurate modeling. Determining these parameters reliably from measured data is a major challenge, for which machine learning approaches offer promising solutions. We provide an overview of these approaches and present our perspective on addressing the inverse problem relating experimental data to ligand-field parameters. Previously, a machine learning architecture combining a variational autoencoder (VAE) and an invertible neural network (INN) showed promise for analyzing temperature-dependent magnetic susceptibility data. In this work, the VAE-INN model is extended through data augmentation to enhance its tolerance to common experimental inaccuracies. Focusing on second-order ligand-field parameters, diamagnetic and molar-mass errors are incorporated by augmenting the training dataset with experimentally motivated error distributions. Tests on simulated experimental susceptibility curves demonstrate substantially improved prediction accuracy and robustness when the distributions correspond to realistic error ranges. When applied to the experimental susceptibility curve of the complex ${\mathrm{Al}}_2^{\mathrm{III}}$${\mathrm{Er}}_2^{\mathrm{III}}$, the augmented VAE–INN recovers ligand-field solutions consistent with least-squares benchmarks. The proposed data augmentation thus overcomes a key limitation, bringing the ML approach closer to practical use for higher-order ligand-field parameters. 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 the solution of equivalent dipoles for inverse electromagnetic problems, the traditional least squares method suffers from ill-conditioned matrices, resulting in insufficient accuracy and anti-noise performance, while existing optimization algorithms tend to fall into local optima during iteration. To address these issues, this paper proposes a phaseless source reconstruction method combining the Adam optimization algorithm with L2 regularization, which can stably solve the equivalent dipole source. The proposed method uses Adam optimization to avoid the direct inversion of ill-conditioned matrices, which improves the accuracy of near-field source reconstruction and effectively avoids falling into local optima. The introduced L2 regularization further suppresses local optima and significantly enhances the anti-noise performance of the equivalent dipole solution. In addition, simulations and experiments are carried out to verify the effectiveness of the proposed method. Full article

Solving Bayesian inverse problems efficiently stands as a major bottleneck in scientific computing. Although Bayesian Physics-Informed Neural Networks (B-PINNs) have introduced a robust way to quantify uncertainty, the high-dimensional parameter spaces inherent in deep learning often lead to prohibitive sampling costs. Addressing this, our work introduces Quantum-Encodable Bayesian PINNs trained via Classical Ensemble Kalman Inversion (QEKI), a framework that pairs Quantum Neural Networks (QNNs) with Ensemble Kalman Inversion (EKI). The core advantage lies in the QNN’s ability to act as a compact surrogate for PDE solutions, capturing complex physics with significantly fewer parameters than classical networks. By adopting the gradient-free EKI for training, we mitigate the barren plateau issue that plagues quantum optimization. Through several benchmarks on 1D and 2D nonlinear PDEs, we show that QEKI yields precise inversions and substantial parameter compression, even in the presence of noise. While large-scale applications are constrained by current quantum hardware, this research outlines a viable hybrid framework for including quantum features within Bayesian uncertainty quantification. Full article

We study an inverse source problem for a semilinear diffusion equation involving a Caputo-type time-fractional derivative whose order is a function of time. The equation is considered in a bounded Lipschitz domain $\mathrm{\Omega }\subset {\mathbb{R}}^d$, $d\ge 1$, and is supplemented with homogeneous Dirichlet boundary conditions. The source term is taken to be separable, $h\left(t\right)f\left(x\right)$, where the temporal component $h\left(t\right)$ is unknown. This quantity is to be identified from spatially localized measurements $m\left(t\right)$ of the solution. In this setting, we establish existence and uniqueness results in suitable function spaces, thereby demonstrating the well-posedness of the corresponding inverse source problem. Full article

Accurate, subject-specific estimation of cervical muscle forces is a critical prerequisite for advancing spinal biomechanics and clinical diagnostics. However, this task remains challenging due to substantial inter-individual anatomical variability and the invasiveness of direct measurement techniques. In this study, we propose a novel data-driven biomechanical framework that addresses these limitations by integrating massive-scale personalized musculoskeletal simulations with an efficient Feedforward Neural Network (FNN) model. We generated an unprecedented dataset comprising one million personalized OpenSim cervical models, systematically varying key anthropometric parameters (neck length, shoulder width, head mass) to robustly capture human morphological diversity. A random subset was selected for inverse dynamics simulations to establish a comprehensive, physics-based training dataset. Subsequently, an FNN was trained to learn a robust, nonlinear mapping from non-invasive kinematic and anthropometric inputs to the forces of 72 cervical muscles. The model’s accuracy was validated on a test set, achieving a coefficient of determination (R²) exceeding 0.95 for all 72 muscle forces. This approach effectively transforms a computationally intensive biomechanical problem into a rapid tool. Additionally, the framework incorporates a functional assessment module that evaluates motion deficits by comparing observed head trajectories against a simulated idealized motion envelope. Validation using data from a healthy subject and a patient with restricted mobility demonstrated the framework’s ability to accurately track muscle force trends and precisely identify regions of functional limitations. This methodology offers a scalable and clinically translatable solution for personalized cervical muscle evaluation, supporting targeted rehabilitation and injury risk assessment based on readily obtainable sensor data. Full article

Under sparse aperture (SA) conditions, inverse synthetic aperture radar (ISAR) imaging becomes a severely ill-posed inverse problem due to undersampled and noisy measurements, leading to pronounced degradation in azimuth resolution and image quality. Although deep learning approaches have demonstrated promising performance for SA-ISAR imaging, their practical deployment is often hindered by black-box behavior, fixed network depth, high computational cost, and limited robustness under extreme operating conditions. To address these challenges, this paper proposes an ADMM Denoising Deep Equilibrium Framework (ADnDEQ) for SA-ISAR imaging. The proposed method reformulates an ADMM-based unfolding process as an implicit deep equilibrium (DEQ) model, where ADMM provides an interpretable optimization structure and a lightweight DnCNN is embedded as a learned proximal operator to enhance robustness against noise and sparse sampling. By representing the reconstruction process as the equilibrium solution of a single-layer network with shared parameters, ADnDEQ decouples forward and backward propagation, achieves constant memory complexity, and enables flexible control of inference iterations. Experimental results demonstrate that the proposed ADnDEQ framework achieves superior reconstruction quality and robustness compared with conventional layer-stacked networks, particularly under low sampling ratios and low-SNR conditions, while maintaining significantly reduced computational cost. 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 paper presents the simultaneous maximization of speed and sensitivity in the Optimal Coordination of Directional Over-Current Protections (OC-DOCP), considering that maximum selectivity is maintained in all solutions. Only these three desirable features of the protection system were considered in the multi-objective approach; thus, the problem can be simply formulated as the weighted sum of speed and sensitivity as goals to be maximized, and the Pareto frontiers correlating speed and sensitivity are easily found in this way. These Pareto frontiers had not been shown in the literature about this topic, and they properly show the compromise solutions for the optimal solutions (i.e., speed improvements imply sensitivity deterioration while sensitivity improvements imply speed degradation). The simplest OC-DOCP formulation, applied to a well-known sample system, is taken as an example to show the Pareto frontiers for different time–current curve types. Another OC-DOCP formulation, which considers different topologies and their probability of occurrence, is also solved and the corresponding Pareto frontiers are also shown. The main findings of this work are the following: (a) in general, the results show that the variation in the speed in the Pareto frontier is more notorious for the less inverse curve types, whose optimal solutions are slower; (b) in the case of extremely inverse curves, the optimal solutions are faster and the effect of changes in sensitivity on the protection speed is very low in the Pareto frontiers; (c) it is also herein shown that the knowledge of this topic is also useful to solve some possible cases of unfeasibility related to the upper bound of time dial settings. Full article

As semiconductor process nodes shrink to 3 nm and beyond, traditional optical proximity correction (OPC) and resolution enhancement technologies (RETs) can no longer meet the high patterning precision needs of advanced chip manufacturing due to the sub-wavelength lithography limits. Inverse lithography technology (ILT), a key part of computational lithography, has become a critical solution for these issues. From an EDA industry perspective, this review provides an original and systematic summary of ILT’s development and applications, which helps integrate the scattered research into a clear framework for both academic and industrial use. Compared with traditional OPC, the latest ILT has three main advantages: (1) better patterning accuracy, as a result of the precise optical models that fix complex optical issues (like diffraction and interference) in advanced lithography systems; (2) a wider process window, as it optimizes mask designs by working backwards from the target wafer patterns, making lithography more stable against process changes; and (3) stronger adaptability to new lithography scenarios, such as High-NA EUV and extended DUV nodes. This review first explains ILT’s working principles (the basic concepts, mathematical formulae, and main methods like level-set and pixelated approaches) and its development history, highlighting key events that boosted its progress. It then analyzes ILT’s current application status in the industry (such as hotspot fixing, full-chip trials, and EUV-era use) and its main bottlenecks: a high computational complexity leading to long runtime, difficulties in mask manufacturing, challenges in model calibration, and a conservative market that slows large-scale adoption. Finally, it discusses promising future directions, including hybrid ILT-OPC-SMO strategies, improving model accuracy, AI/ML-driven design, GPU acceleration, multi-beam mask writer improvements, and open-source data to solve data shortage problems. By combining the latest research and industry practices, this review fills the gap of comprehensive ILT summaries that cover the principles, progress, applications, and prospects. It helps readers fully understand ILT’s technical landscape and offers practical insights for solving the key challenges, thus promoting ILT’s industrial use in advanced chip manufacturing. Full article