In this research work, a novel deep learning framework is suggested to recognize highly connected acoustic signals from a noisy mixture for enhancing the reliability and clarity of underwater communication. At first, essential Underwater Acoustic Signals (UAS) are collected from the standard resources. Then, the gathered signals are given to the noise reduction phase for enhancing the signal clarity. Here, noises presented in the UAS are reduced using the developed Adaptive Residual Autoencoder with Spatial-Temporal Attention (AResASTA) model. Further, the parameters in the proposed AResAe-STA are tuned using the Renovated Random Attribute-based Golf Optimization Algorithm (RRA-GOA). It can effectively handle large volumes of data promptly to generate optimal solutions. This allows the clear detection of UAS, leading to improved signal recognition and classification. At last, the noise reduction outcomes are attained from the developed AResAe-STA mechanism. Further, various performance measures are used to optimally validate the system performance, and it is compared with several existing methods to observe its effectiveness. The proposed method’s overall performance is maximized by 7.49% of DPTN, 5.47% of DPRN, 3.21% of BSS, and 1.05% of AResASTA in terms of the PCC measure.

In this study, we propose two robust computational schemes for solving the well-known strongly nonlinear Bratu and Lane–Emden-type equations, with applications to combustion and astrophysics. The proposed quasi-linearized Picard iteration method (QPIM) combines the quasi-linearization technique with the Picard iteration, while its piecewise extension is uniform and significantly enhances the convergence region and improves stability near singularity. In QPIM, quasi-linearization transforms a nonlinear equation into a sequence of linearized problems, which are then efficiently solved using the Picard approach. Unlike existing approaches such as Adomian decomposition, Taylor wavelets, or block Nyström methods, the proposed schemes achieve highly accurate solutions with only a few iterations, even over large intervals. Comprehensive numerical experiments on Bratu and Lane–Emden equations demonstrate that QPIM and piecewise QPIM yield up to several orders of magnitude smaller errors compared to existing methods, confirming their superiority in terms of accuracy, efficiency, and ease of implementation.

Reliability-Based Design Optimization (RBDO) provides an effective framework for addressing reliability constraints induced by uncertainties. Conventional RBDO approaches commonly employ the First-Order Reliability Method (FORM) for reliability estimation, which inevitably introduces first-order approximation errors. To overcome this limitation, this study proposes a Sequential Failure Probability Boundary Approximation (SFPBA) method, in which Monte Carlo Simulation (MCS) is employed to obtain accurate evaluations of failure probabilities, while the limit state surface is used to approximate the true failure probability boundary in the vicinity of the optimum. The proposed method effectively addresses the deficiencies of FORM in dealing with nonlinear problems, thereby enhancing the accuracy of solutions in nonlinear RBDO applications. The effectiveness and efficiency of the methodology are demonstrated through two numerical examples.

The nonprobabilistic convex model is suitable for handling many engineering structures with limited information. Recently, the generalization of the conventional interval and ellipsoidal models has received more attention, which provides more flexibility and may possess more compact uncertainty domain. In this paper, a novel generalization of both the interval model and the ellipsoidal model, namely the interval and ellipsoid intersection model, is proposed to achieve more accurate approximation for experimental data. The proposed model can provide a smaller uncertainty domain and can achieve a better balance between accuracy and efficiency than both the interval model and the ellipsoidal model. Based on the proposed model, a semi-analytical method is developed to efficiently obtain the bounds of linear or weak nonlinear response functions, and a nonprobabilistic reliability index is proposed to rationally assess the safety degree of structures. Three numerical examples are provided to demonstrate the effectiveness of the proposed model, to illustrate the superiority of the semi-analytical method over the interior-point method and the rationality of the proposed nonprobabilistic reliability index.

Red Blood Cell (RBC) deformability refers to the ability of RBCs to change their shape in response to external forces. This deformation plays a crucial role in altering the flow conditions within blood vessels, which in turn reduces the resistance to blood flow. RBC deformation is primarily caused by shear stress within the blood circulation. Various methods have been developed to measure RBC deformability, but these techniques often require specialized equipment, lengthy measurement times, and highly skilled personnel. So, to address these challenges, the novel technique, Gannet Puffer fish Optimization Algorithm with the Pyramid Network (GPOA_PyramidNet) is developed in this research for RBC deformability using microscopic images. Initially, the microscopic image from the Federated Research Data Repository (FRDR) is taken as an input. Then, the image enhancement is performed by the technique called Contract Limited Adaptive Histogram Equalization (CLAHE). Consequently, cell segmentation is carried out using the entropy-based Kapur methodology, in which GPOA selects the threshold values. The proposed GPOA is the fusion of the Pufferfish Optimization Algorithm (POA) and the Gannet Optimization Algorithm (GOA). Later, the features, like Gray-Level Co-occurrence Matrix (GLCM) and shape features are extracted. Then, the RBC deformability is achieved using the GPOA_PyramidNet, and they are classified as rigid RBCs and deformable RBCs. The proposed GPOA_PyramidNet is analyzed for its effectiveness in terms of metrics like accuracy, True Positive Rate (TPR), and True Negative Rate (TNR). It is found that the proposed method attained a maximum accuracy of 92.88%, TPR of 95.79%, and TNR of 93.90%, which is superior to the prevailing techniques. Moreover, the proposed GPOA_PyramidNet model achieves higher accuracy compared to several other methods, with improvements of 16.03% over Convolutional Neural Network (CNN), 11.84% over Convolution and Recurrent Neural Network (C-RNN), 7.52% over CNN-ALL, 2.13% over Variational Autoencoder (VAE), 1.52% over Image-based RBC deformability assessment via a shape-classification approach (IRIS), 1.08% over Light Weight Convolutional Neural Network (LWCNN), 0.96% over Region-based Convolutional Neural Network (RCNN), and 0.57% over ICAFF-MobileNetv2.

The goal of this paper is to create a reliable and effective numerical scheme for solving a system of second-order singularly perturbed convection–diffusion type turning point problem. The boundary layer is found to arise on the left side of the spatial domain by closely examining the coefficients of the convection term in the coupled system of equations. Initially, the Crank–Nicolson approach is used to semi-discrete version of the problem in time direction. Next we use a trigonometric cubic B-spline (TCBS) collocation approach on a properly designed Shishkin mesh in the spatial direction to discretize the resulting semi-discrete system. The convergence analysis presented in this paper demonstrates that the proposed method achieves an order of convergence close to two, with an error estimate of order [Formula: see text] A numerical example is provided to validate and illustrate the theoretical findings.

In science and engineering, advection and diffusion processes are integral to numerous applications, ranging from fluid dynamics and hydraulics to groundwater contamination, oil reservoir management, chemical separation, semiconductor modeling, and air transport. This paper introduces mesh-free approaches based on radial basis functions for the simulation of the 2D unsteady advection–diffusion equation. The development of the first approach begins with the discretization of the time derivative using a forward finite difference method, followed by an analysis of the stability and convergence of the semi-discrete model in [Formula: see text] and [Formula: see text] spaces. The fully discrete model is then obtained by applying the local radial basis function differential quadrature approach. In the second numerical approach, LRBF-DQA is initially applied to approximate the spatial derivatives, leading to a system of nonlinear ordinary differential equations (ODEs). The system is then solved using the RK4 method, and the stability of the approach is assessed through the matrix method. Numerical experiments demonstrate that the proposed approaches are both accurate and computationally efficient.

In recent years, physics-informed neural network (PINN) has gained attention as a novel approach for solving partial differential equations. By embedding physical constraints, such as conservation laws and boundary conditions, into the loss function, the model’s adaptability to physical problems is enhanced, yielding more precise solutions. However, PINN often produces smooth results, making it challenging to solve problems involving strong discontinuities like shock wave. To improve the accuracy of PINN in capturing shocks, this paper proposes an adaptive weighted multi-physics-informed neural network (AW-MPINN). To address numerical instability and convergence issues caused by gradient imbalance among constraint terms during training, the weights of these terms are dynamically optimized based on gradient variations, enabling the model to flexibly respond to changes and balance loss contributions in discontinuous regions. Additionally, weight coefficients are constrained using gradient clipping to reduce optimization bias caused by weight fluctuations. The proposed AW-MPINN is evaluated on three benchmark problems. Compared to nonadaptive methods, it achieves sharper discontinuity resolution and improved accuracy under limited training data; when tested against existing adaptive approaches, it demonstrates faster convergence and more stable loss balancing, leading to enhanced robustness and shock-capturing capability.

Computational fluid dynamics (CFD) is still the most widely used method for determining the flow inside the turbomachinery, but high-fidelity simulations are typically time-consuming, particularly when multi-parameter optimization, design, and other issues are involved. The reduced-order model (ROM) is able to tackle these issues. In this paper, a nonintrusive reduced-order model based on numerical simulations is developed using direct proper orthogonal decomposition (POD) and radial basis function (RBF) interpolation. POD can realize the data dimension reduction and get the mode coefficients related to the parameters; RBF is used to establish the mapping relationship from the parameters to the mode coefficients and finally achieve the flow field prediction. In order to improve the efficiency and accuracy of the model, the traditional structure of the snapshot matrix is changed so that the user only needs to perform a POD decomposition once to decouple the parameters, while the particle swarm optimization (PSO) algorithm is applied to optimize the width factor of the radial basis function. The POD-RBF-ROM (PR-ROM) proposed in this paper accomplishes a highly accurate prediction of the unsteady flow field of a 1.5-stage compressor, achieving an average prediction error of approximately 2%, with the maximum error for any individual case not exceeding 9%. Compared with a single CFD simulation, the computational efficiency of the PR-ROM online stage has been improved by at least five orders of magnitude, but this comes at the expense of the offline training stage, which requires sufficient high-fidelity snapshots to be pre-calculated.

In this paper, an efficient finite difference scheme is investigated for the two-dimensional semi-linear time–space fractional diffusion-wave equations that have solutions with weak singularity in time–direction at the initial time. First, the original equation is transformed into a system of two equations with the Caputo derivatives of the same order between 0 and 1 by using the symmetric fractional-order reduction method. Then, the Caputo derivative is discretized by the L1 scheme on the nonuniform meshes, and the Riesz derivatives are discretized by the second-order weighted and shifted Grünwald scheme. Newton’s method is used to linearize the nonlinear term. For the resulting linearized finite difference scheme, in the discrete [Formula: see text]-norm, the unconditional stability is analyzed and the optimal error estimate is derived. It is demonstrated that the proposed scheme can be efficiently solved by using the conjugate gradient method, and some numerical experiments are given to verify the theoretical results.