Search Results (70)

This work proposes an analysis of the capability of three deep learning models—the feedforward neural network (FFNN), long short-term memory (LSTM) network, and physics-informed neural network (PINN)—to identify the parameters of a flexible fixed-wing aircraft using in-flight data. These neural networks, composed of multiple hidden layers, are evaluated for their ability to perform system identification and to capture the nonlinear and dynamic behavior of the aircraft. The FNN and LSTM models are compared to assess the impact of temporal dependency learning on parameter estimation, while the PINN integrates prior knowledge of the system’s governing of ordinary differential equations (ODEs) to enhance physical consistency in the identification process. The objective is to exploit the generalization capability of neural network-based models while preserving the accurate estimation of the physical parameters that characterize the analyzed system. The neural networks are evaluated for their ability to perform system identification and capture the nonlinear behavior of the aircraft. The results show that the FFNN achieved the best overall performance, with average Theil’s inequality coefficient (TIC) values of 0.162 during training and 0.386 during testing, efficiently modeling the input-output relationships but tending to fit high-frequency measurement noise. The LSTM network demonstrated superior noise robustness due to its temporal filtering capability, producing smoother predictions with average TIC values of 0.398 (training) and 0.408 (testing), albeit with some amplitude underestimation. The PINN, while successfully integrating physical constraints through pretraining with target aerodynamic derivatives, showed more complex convergence, with average TIC values of 0.243 (training) and 0.475 (testing), and its estimated aerodynamic coefficients differed significantly from the conventional values. All three architectures effectively captured the coupled rigid-body and flexible dynamics when trained with distributed wing sensor data, demonstrating that neural network-based approaches can model aeroelastic phenomena without requiring explicit high-fidelity flexible-body models. This study provides a comparative framework for selecting appropriate neural network architectures based on the specific requirements of aircraft system identification tasks. Full article

This study examines the nonlinear dynamical behavior of a Van der Waals system in the viscosity–capillarity regularization form. The solitary wave solutions of the proposed model are investigated using advanced analytical techniques, including the generalized Arnous method, the modified generalized Riccati equation mapping method, and the modified F-expansion approach. Additionally, we use mathematical simulations to enhance our comprehension of wave propagation. Moreover, a machine learning algorithm known as the multilayer perceptron regressor neural network was adopted to predict the performance results of our soliton solutions. Another important aspect of this study is the exploration of the chaos of the studied model by introducing a perturbed system. Chaotic analysis is supported by different techniques, such as return maps, power spectra, a bifurcation diagram, and a chaotic attractor. This multifaceted investigation not only emphasizes the rich dynamical pattern of the studied model but also presents a robust mathematical framework for studying nonlinear systems. The studied model also presents a robust mathematical framework for studying nonlinear systems. This study offers novel insights into nonlinear dynamics and wave phenomena by assessing the effectiveness of modern methodologies and clarifying the distinctive characteristics of a system’s nonlinear dynamics. Full article

Accurate and efficient CFD simulations are essential for a wide range of engineering and scientific applications, from resilient structural design to environmental analysis. Traditional methods such as RANS simulations often face challenges in capturing complex flow phenomena like separation, while high-fidelity approaches including Large Eddy Simulations and Direct Numerical Simulations demand significant computational resources, thereby limiting their practical applicability. This paper provides an in-depth synthesis of recent advancements in integrating artificial intelligence and machine learning techniques with CFD to enhance simulation accuracy, computational efficiency, and modeling capabilities, including data-driven surrogate models, physics-informed methods, and ML-assisted numerical solvers. This integration marks a crucial paradigm shift, transcending incremental improvements to fundamentally redefine the possibilities of fluid dynamics research and engineering design. Key themes discussed include data-driven surrogate models, physics-informed methods, ML-assisted numerical solvers, inverse design, and advanced turbulence modeling. Practical applications, such as wind load design for solar panels and deep learning approaches for eddy viscosity prediction in bluff body flows, illustrate the substantial impact of ML integration. The findings demonstrate that ML techniques can accelerate simulations by up to 10,000 times in certain cases while maintaining or improving the accuracy, particularly in challenging flow regimes. For instance, models employing learned interpolation can achieve 40- to 80-fold computational speedups while matching the accuracy of baseline solvers with a resolution 8 to 10 times finer. Other approaches, like Fourier Neural Operators, can achieve inference times three orders of magnitude faster than conventional PDE solvers for the Navier–Stokes equations. Such advancements not only accelerate critical engineering workflows but also open unprecedented avenues for scientific discovery in complex, nonlinear systems that were previously intractable with traditional computational methods. Furthermore, ML enables unprecedented advances in turbulence modeling, improving predictions within complex separated flow zones. This integration is reshaping fluid mechanics, offering pathways toward more reliable, efficient, and resilient engineering solutions necessary for addressing contemporary challenges. Full article

This study introduces a memristive Hopfield neural network (M-HNN) model to investigate electromagnetic radiation impacts on neural dynamics in complex electromagnetic environments. The proposed framework integrates a magnetic flux-controlled memristor into a three-neuron Hopfield architecture, revealing significant alterations in network dynamics through comprehensive nonlinear analysis. Numerical investigations demonstrate that memristor-induced electromagnetic effects induce distinctive phenomena, including coexisting attractors, transient chaotic states, symmetric bifurcation diagrams and attractor structures, and constant chaos. The proposed system can generate more than 12 different attractors and extends the chaotic region. Compared with the chaotic range of the baseline Hopfield neural network (HNN), the expansion amplitude reaches 933%. Dynamic characteristics are systematically examined using phase trajectory analysis, bifurcation mapping, and Lyapunov exponent quantification. Experimental validation via a DSP-based hardware implementation confirms the model’s operational feasibility and consistency with numerical predictions, establishing a reliable platform for electromagnetic–neural interaction studies. Full article

In the present paper, a mathematical analysis of the Gardner equation with varying coefficients has been performed to give a more realistic model of physical phenomena, especially in regards to plasma physics. First, a Lie symmetry analysis was carried out, as a result of which a symmetry classification following the different representations of the variable coefficients was systematically derived. The reduced ordinary differential equation obtained is solved using the power-series method and solutions to the equation are represented graphically to give an idea of their dynamical behavior. Moreover, a fully connected neural network has been included as an efficient computation method to deal with the complexity of the reduced equation, by using traveling-wave transformation. The validity and correctness of the solutions provided by the neural networks have been rigorously tested and the solutions provided by the neural networks have been thoroughly compared with those generated by the Runge–Kutta method, which is a conventional and well-recognized numerical method. The impact of a variation in the loss function of different coefficients has also been discussed, and it has also been found that the dispersive coefficient affects the convergence rate of the loss contribution considerably compared to the other coefficients. The results of the current work can be used to improve knowledge on the nonlinear dynamics of waves in plasma physics. They also show how efficient it is to combine the approaches, which consists in the use of analytical and semi-analytical methods and methods based on neural networks, to solve nonlinear differential equations with variable coefficients of a complex nature. Full article

Piezoelectric actuators are commonly used in high precision, micro-displacement applications. However, nonlinear phenomena, like hysteresis, may reduce their performance. This article compares several control approaches—based on the combination of sliding mode control and artificial neural networks—for coping with these nonlinearities and improving actuator positioning accuracy and robustness. In particular, it discusses the application of diverse order sliding mode control techniques, such as conventional, twisting algorithms, super-twisting algorithms, and the prescribed convergence law, in combination with artificial neural networks. Moreover, it validates experimentally, with a commercial piezoelectric actuator, the application of these control structures using a dSPACE 1104 controller board. Finally, it evaluates the computational time consumption for the control strategies presented. This work intends to guide the designers of PEA commercial applications to select the best control algorithm and identify the hardware requirements. Full article

Background: The Bullwhip and Ripple effects are systemic phenomena that disrupt supply chain performance. However, research often neglects their connection to resilience. This article presents a hybrid literature review examining how both effects are addressed about supply chain resilience, focusing on methodological and conceptual trends. Methods: The review combines thematic analysis of studies from Web of Science and ScienceDirect (2000–2023) with bibliometric trend modeling using Long Short-Term Memory neural networks to detect nonlinear patterns and disciplinary dynamics. Results: While 64.7% of the reviewed works explicitly link the Bullwhip Effect or Ripple Effect to resilience, only 11.7% of those focused on the Bullwhip Effect offer models with clear practical use. A structural break in 2019 marks a notable rise in research connecting these effects to resilience. Nonlinear modeling dominates (88.23%) through network theory and system dynamics. Social, Engineering and Business Sciences drive Bullwhip-related studies, while Economics, Computer Science, and Social Sciences lead Ripple-related research. Business, Energy, and Social Sciences strongly influence the integration of the Ripple Effect into supply chains. A modeling typology is proposed, and neural network techniques uncover key bibliometric patterns. Conclusions: The review highlights limited practical application and calls for more adaptive, integrative research approaches. Full article

Background: In functional magnetic resonance imaging (fMRI), functional network connectivity (FNC) captures temporal coupling among intrinsic connectivity networks (ICNs). Traditional FNC analyses often rely on linear models, which may overlook complex nonlinear interactions. We propose a multi-layered neural network that generates nonlinear heatmaps from FNC matrices, which we visualize at multiple layers, enabling us to better characterize multi-level interactions and improve interpretability. Methods: Our approach consists of two training stages. In the first, a deep convolutional neural network (DCNN) is trained to produce heatmaps from multiple convolution layers. In the second, a t-test-based feature selection identifies relevant heatmaps that help distinguish different groups. In addition, we introduce ‘source-based features’ which summarize the multi-layer model output using an independent component analysis-based procedure that provides valuable, interpretable insights into the specific layer outputs. We tested this approach on a large dataset of schizophrenia patients and healthy controls, split into training and validation sets. Furthermore, this method clarifies how underlying neural mechanisms differ between schizophrenia patients and healthy controls, revealing crucial patterns in the default mode and visual networks. Results: The results indicate increased default mode network connectivity with itself and cognitive control regions in patients, while controls showed stronger visual and sensorimotor connectivity. Our DCNN approach achieved 92.8% cross-validated classification accuracy, outperforming competing methods. We also separated individuals into three cognitive performance groups based on cognitive scores and showed that the model can accurately predict the cognitive level using the FNC data. Conclusion: Our novel approach demonstrates the advantage of employing more sophisticated models in characterizing complex brain connectivity patterns while enhancing the interpretability of results. These findings underscore the significance of modeling nonlinear dynamics in fMRI analysis, shedding new light on the intricate interplays underlying cognitive and psychiatric phenomena. Full article

Against the background of globalization, the circulation range of traditional Chinese medicinal materials is constantly expanding, and the phenomena of mixed origins and counterfeiting are becoming increasingly serious. Tracing the origin of traditional Chinese medicinal materials is of great significance for ensuring their quality, safety, and effectiveness. Laser-induced breakdown spectroscopy (LIBS), as a rapid and non-destructive element analysis technique, can be used for the origin tracing of traditional Chinese medicinal materials. Deep learning can not only handle non-linear relationships but also automatically extract features from high-dimensional data. In this paper, LIBS is combined with deep learning, and a Double-Multi Convolutional Neural Network LIBS Analysis System (DMC-LIBSAS) is proposed for the origin tracing of the traditional Chinese medicinal material Angelica dahurica. The system consists of a LIBS signal generation module, a spectral preprocessing module, and an algorithm analysis module—Double-Multi Convolutional Neural Network (DMCNN)—achieving a direct mapping from input data to output results. And the ability of DMCNN to extract characteristic peaks is demonstrated by the 1D Gradient-weighted Class Activation Mapping (1D-Grad-CAM) method. The tracing accuracy of DMC-LIBSAS for Angelica dahurica reaches 95.25%. To further verify the effectiveness of the system, it is compared with six classic methods including LeNet, AlexNet, Resnet18, K-nearest neighbors (KNN), Random Forest (RF), and Decision Tree (DT) (with accuracies of 68%, 75%, 72.5%, 79.7%, 86.7%, and 75.5%, respectively), and the tracing effects are all much lower than that of DMC-LIBSAS. The results show that DMC-LIBSAS can effectively and accurately trace the origin of Angelica dahurica, providing a new technical support for the quality supervision of traditional Chinese medicinal materials. Full article

Anomalous diffusion is characterized by nonlinear growth in the mean square displacement of a trajectory. Recent advances using statistical methods and recurrent neural networks have made it possible to detect such phenomena, even in noisy conditions. In this work, we explore feature extraction through parametric and non-parametric spectral analysis methods to decode anomalously diffusing trajectories, achieving reduced computational costs compared with other approaches that require additional data or prior training. Specifically, we propose the use of higher-order statistics, such as the bispectrum, and a hybrid algorithm that combines kurtosis with a multiple-signal classification technique. Our results demonstrate that the type of trajectory can be identified based on amplitude and kurtosis values. The proposed methods deliver accurate results, even with short trajectories and in the presence of noise. Full article

This study aimed to identify the correlation between global climate phenomena, such as the ENSO, and South Korea’s Consumer Price Index (CPI) for a climate-sustainable economy. South Korea’s CPI has shown a linear upward trend, prompting a trend analysis and the subsequent removal of the linear trend for further examination. The correlation analysis identified statistically significant cases under the study’s criteria, with the Southern Oscillation Index (SOI) displaying the highest contribution and sensitivity. When comparing general correlations, the strongest relationship was observed with a 27-month lag. The Granger Causality Test, however, revealed causality with a 9-month lag between the CPI and El Niño–Southern Oscillation (ENSO) indices. This indicates the feasibility of separate analyses for long-term (27 months) and short-term (9 months) impacts. The correlation analysis confirmed that the ENSO contributes to explainable variations in the CPI, suggesting that CPI fluctuations could be predicted based on ENSO indices. Utilizing ARIMA models, the study compared predictions using only the CPI’s time series against an ARIMAX model that incorporated SOI and MEI as exogenous variables with a 9-month lag. Using the ARIMA model, this study compared predictions based solely on the time series of CPI with the ARIMAX model, which incorporated SOI and MEI as exogenous variables with a 9-month lag. Furthermore, to investigate nonlinear teleconnections, the neural network model LSTM was applied for comparison. The analysis results confirmed that the model reflecting nonlinear teleconnections provided more accurate predictions. These findings demonstrate that global climate phenomena can significantly influence South Korea’s CPI and provide experimental evidence supporting the existence of nonlinear teleconnections. This study highlights the meaningful correlations between climate indices and CPI, suggesting that climate variability affects not only weather conditions but also economic factors in a country. Full article

This study employs a novel physics-informed neural network (PINN) approach, the standard explicit finite difference method (EFDM) and unconditionally positivity preserving FDM to tackle the one-dimensional Sine–Gordon equation (SGE). Two test problems with known analytical solutions are investigated to demonstrate the effectiveness of these techniques. While the three employed approaches demonstrate strong agreement, our analysis reveals that the EFDM results are in the best agreement with the analytical solutions. Given the consistent agreement between the numerical results from the EFDM, unconditionally positivity preserving FDM and PINN approach and the analytical solutions, all three methods are recommended as competitive options. The solution techniques employed in this study can be a valuable asset for present and future model developers engaged in various nonlinear physical wave phenomena, such as propagation of solitons in optical fibers. Full article

The increasing complexity of social science data and phenomena necessitates using advanced analytical techniques to capture nonlinear relationships that traditional linear models often overlook. This chapter explores the application of machine learning (ML) models in social science research, focusing on their ability to manage nonlinear interactions in multidimensional datasets. Nonlinear relationships are central to understanding social behaviors, socioeconomic factors, and psychological processes. Machine learning models, including decision trees, neural networks, random forests, and support vector machines, provide a flexible framework for capturing these intricate patterns. The chapter begins by examining the limitations of linear models and introduces essential machine learning techniques suited for nonlinear modeling. A discussion follows on how these models automatically detect interactions and threshold effects, offering superior predictive power and robustness against noise compared to traditional methods. The chapter also covers the practical challenges of model evaluation, validation, and handling imbalanced data, emphasizing cross-validation and performance metrics tailored to the nuances of social science datasets. Practical recommendations are offered to researchers, highlighting the balance between predictive accuracy and model interpretability, ethical considerations, and best practices for communicating results to diverse stakeholders. This chapter demonstrates that while machine learning models provide robust solutions for modeling nonlinear relationships, their successful application in social sciences requires careful attention to data quality, model selection, validation, and ethical considerations. Machine learning holds transformative potential for understanding complex social phenomena and informing data-driven psychology, sociology, and political science policy-making. Full article

This study investigated the ability of artificial neural networks (ANNs) to resolve the nonlinear dynamics inherent in the behavior of complex fluid flows, which often exhibit multifaceted characteristics that challenge traditional analytical or numerical methods. By employing flow profile pairs that are generated through high-fidelity numerical simulations, encompassing both the one-dimensional benchmark problems and the more intricate three-dimensional boundary layer transition problem, this research convincingly demonstrates that neural networks possess a remarkable capacity to effectively capture the discontinuities and the subtle wave characteristics that occur at small scales within complex fluid flows, thereby showcasing their robustness in handling intricate fluid dynamics phenomena. Furthermore, even in the context of challenging three-dimensional problems, this study reveals that the average velocity profiles can be predicted with a high degree of accuracy, utilizing a limited number of input profiles during the training phase, which underscores the efficiency and efficacy of the model in understanding complex systems. The findings of this study significantly underscore the immense potential that artificial neural networks, along with deep learning methodologies, hold in advancing our comprehension of the fundamental physics that govern complex fluid dynamics systems, while concurrently demonstrating their applicability across a variety of flow scenarios and their capacity to yield insightful revelations regarding the nonlinear relationships that exist among diverse flow parameters, thus paving the way for future research in this critical area of study. Full article

Fractional calculus plays a pivotal role in modern scientific and engineering disciplines, providing more accurate solutions for complex fluid dynamics phenomena due to its non-locality and inherent memory characteristics. In this study, Caputo’s time fractional derivative operator approach is employed for heat and mass transfer modeling in unsteady Maxwell fluid within a cylinder. Governing equations within a cylinder involve a system of coupled, nonlinear fractional partial differential equations (PDEs). A machine learning technique based on the Levenberg–Marquardt scheme with a backpropagation neural network (LMS-BPNN) is employed to evaluate the predicted solution of governing flow equations up to the required level of accuracy. The numerical data sheet is obtained using series solution approach Homotopy perturbation methods. The data sheet is divided into three portions i.e., $80\%$ is used for training, $10\%$ for validation, and $10\%$ for testing. The mean-squared error (MSE), error histograms, correlation coefficient (R), and function fitting are computed to examine the effectiveness and consistency of the proposed machine learning technique i.e., LMS-BPNN. Moreover, additional error metrics, such as R-squared, residual plots, and confidence intervals, are incorporated to provide a more comprehensive evaluation of model accuracy. The comparison of predicted solutions with LMS-BPNN and an approximate series solution are compared and the goodness of fit is found. The momentum boundary layer became higher and higher as there was an enhancement in the value of Caputo, fractional order α = 0.5 to α = 0.9. Higher thermal boundary layer (TBL) profiles were observed with the rising value of the heat source. Full article