Search Results (235)

The core challenge of the Unique Continuity (UC) problem lies in inferring solutions across an entire domain using limited observational data, holding significant practical implications for multiphysics coupled models. Recently, physics-informed neural networks (PINNs) have shown considerable promise in addressing the UC problem. However, the reliance on a fixed activation function and a fixed weighted loss function prevents PINNs from adequately representing the multiphysics characteristics embedded in coupled models. To overcome these limitations, we propose a novel dual adaptive neural network (DANN) algorithm. This approach integrates trainable adaptive activation functions and an adaptively weighted loss scheme, enabling the network to dynamically balance the observational data and governing physics. Our method is applicable not only to the UC problem but also to general forward problems governed by partial differential equations. Furthermore, we provide a theoretical foundation for the algorithm by deriving a generalization error estimate, discussing the potential causes of neural networks solving this problem. Extensive numerical experiments including 3D demonstrate the superior accuracy and effectiveness of the proposed DANN framework in solving the UC problem compared to standard PINNs. Full article

The integration of artificial intelligence (AI) and machine learning (ML) has revolutionised civil engineering, enhancing predictive accuracy, decision-making, and sustainability across domains such as structural health monitoring, geotechnical analysis, transportation systems, water management, and sustainable construction. This paper presents a detailed review of peer-reviewed publications from the past decade, employing bibliometric mapping and critical evaluation to analyse methodological advances, practical applications, and limitations. A novel taxonomy is introduced, classifying AI/ML approaches by civil engineering domain, learning paradigm, and adoption maturity to guide future development. Key applications include pavement condition assessment, slope stability prediction, traffic flow forecasting, smart water management, and flood forecasting, leveraging techniques such as Convolutional Neural Networks (CNNs), Long Short-Term Memory (LSTM), Support Vector Machines (SVMs), and hybrid physics-informed neural networks (PINNs). The review highlights challenges, including limited high-quality datasets, absence of AI provisions in design codes, integration barriers with IoT-based infrastructure, and computational complexity. While explainable AI tools like SHAP and LIME improve interpretability, their practical feasibility in safety-critical contexts remains constrained. Ethical considerations, including bias in training datasets and regulatory compliance, are also addressed. Promising directions include federated learning for data privacy, transfer learning for data-scarce regions, digital twins, and adherence to FAIR data principles. This study underscores AI as a complementary tool, not a replacement, for traditional methods, fostering a data-driven, resilient, and sustainable built environment through interdisciplinary collaboration and transparent, explainable systems. Full article

This paper addresses first- and second-kind Volterra integral equations (VIEs) with discontinuous kernels. A hybrid method combining the Homotopy Analysis Method (HAM) and Physics-Informed Neural Networks (PINNs) is developed. The convergence of the HAM is analyzed. Benchmark examples confirm that the proposed HAM-PINNs approach achieves high accuracy and robustness, demonstrating its effectiveness for complex kernel structures. Full article

Nonlinear complex systems exhibit emergent behavior, sensitivity to initial conditions, and rich dynamics arising from interactions among their components. A classical example of such a system is the Troesch problem—a nonlinear boundary value problem with wide applications in physics and engineering. In this work, we investigate and compare two distinct approaches to solving this problem: the Differential Transform Method (DTM), representing an analytical–symbolic technique, and Physics-Informed Neural Networks (PINNs), a neural computation framework inspired by physical system dynamics. The DTM yields a continuous form of the approximate solution, enabling detailed analysis of the system’s dynamics and error control, whereas PINNs, once trained, offer flexible estimation at any point in the domain, embedding the physical model into an adaptive learning process. We evaluate both methods in terms of accuracy, stability, and computational efficiency, with particular focus on their ability to capture key features of nonlinear complex systems. The results demonstrate the potential of combining symbolic and neural approaches in studying emergent dynamics in nonlinear systems. Full article

Sea surface salinity (SSS) observations play a crucial role in the study of ocean circulation, climate variability, and marine ecosystems. However, current satellite SSS products suffer from systematic biases due to factors such as radio frequency interference (RFI) and land contamination, resulting in fundamental limitations to their application for SSS monitoring. To address this issue, we propose a physics-informed neural network (PINN) approach that directly integrates radiative transfer physical processes into the neural network architecture for SMAP L2 SSS bias correction. This method ensures oceanographically consistent corrections by embedding physical constraints into the forward propagation model. The results demonstrate that PINN achieved a root mean square error (RMSE) of 0.249 PSU, representing a 5.3% to 8.5% relative performance improvement compared to conventional methods—GBRT, ANN, and XGBoost. Further temporal stability analysis reveals that PINN exhibits significantly reduced RMSE variations over multi-year periods, demonstrating exceptional long-term correction stability. Meanwhile, this method achieves more uniform bias improvement in contaminated nearshore regions, showing distinct advantages over the inconsistent correction patterns of conventional methods. This study establishes a physics-constrained machine learning framework for satellite SSS data correction by integrating oceanographic domain knowledge, providing a novel technical pathway for reliable enhancement of Earth observation data. Full article

An accurate perception of upper-level wind fields is essential for improving civil aviation safety and route optimization. However, the sparsity of observational data and the structural complexity of wind fields make reconstruction highly challenging. To address this, we propose QuadMamba-WindNet (QMW-Net), a structure-enhanced deep neural network that integrates a hierarchical state-space modeling framework with a learnable quad-tree-based regional partitioning mechanism, enabling multi-scale adaptive encoding and efficient dynamic modeling. The model is trained end-to-end on ERA5 reanalysis data and validated with simulated flight trajectory observation masks, allowing the reconstruction of complete horizontal wind fields at target altitude levels. Experimental results show that QMW-Net achieves a mean absolute error (MAE) of 1.62 m/s and a mean relative error (MRE) of 6.68% for wind speed reconstruction at 300 hPa, with a mean directional error of 4.85° and an $R^2$ of 0.93, demonstrating high accuracy and stable error convergence. Compared with Physics-Informed Neural Networks (PINNs) and Gaussian Process Regression (GPR), QMW-Net delivers superior predictive performance and generalization across multiple test sets. The proposed model provides refined wind field support for civil aviation forecasting and trajectory planning, and shows potential for broader applications in high-dynamic flight environments and atmospheric sensing. Full article

This paper considers the possibility of using Physics-Informed Neural Networks (PINNs) to study the hydrological processes of model river sections. A fully connected neural network is used for the approximation of the Saint-Venant equations in both 1D and 2D formulations. This study addresses the problem of determining the velocities, water level, discharge, and area of water sections in 1D cases, as well as the inverse problem of calculating the roughness coefficient. To evaluate the applicability of PINNs for modeling flows in channels, it seems reasonable to start with cases where exact reference solutions are available. For the 1D case, we examined a rectangular channel with a given length, width, and constant roughness coefficient. An analytical solution is obtained to calculate the discharge and area of the water section. Two-dimensional model examples were also examined. The synthetic data were generated in Delft3D code, which included velocity field and water level, for the purpose of PINN training. The calculation in Delft3D code took about 2 min. The influence of PINN hyperparameters on the prediction quality was studied. Finally, the absolute error value was assessed. The prediction error of the roughness coefficient n value in the 2D case for the inverse problem did not exceed 10%. A typical training process took from 2.5 to 3.5 h and the prediction process took 5–10 s using developed PINN models on a server with Nvidia A100 40GB GPU. Full article

We present a Physics-Informed Neural Network (PINN) approach to solving the Lane–Emden equation, a model used to describe polytropic stars’ behavior in astrophysics. The equation is reformulated as a two-dimensional problem; we treat both the radial coordinate and polytropic index as inputs for the neural network. In order to improve stability and accuracy, we introduced coordinate embedding via Random Fourier Features, residual blocks, and gating mechanisms. Experiments show that our neural networks outperform other traditional numerical methods, including Monte Carlo simulations and standard fully connected PINNs. We achieve accurate predictions for both trained and extrapolated polytropic indices. The code used to implement our method is publicly available providing researchers with the resources to replicate and extend our work. Full article

High-Voltage Alternating Current (HVAC) transmission systems form the backbone of modern power grids, enabling efficient long-distance and high-capacity power delivery. In Saudi Arabia, ongoing initiatives to modernize and strengthen grid infrastructure demand advanced solutions to ensure system reliability, operational stability, and the minimization of economic losses caused by faults. Traditional fault detection and classification methods often depend on the manual interpretation of voltage and current signals, which is both labor-intensive and prone to human error. Although data-driven approaches such as Artificial Neural Networks (ANNs) and Deep Learning have been applied to automate fault analysis, their performance is often constrained by the quality and size of available training datasets, leading to poor generalization and physically inconsistent outcomes. This study proposes a novel hybrid fault detection and classification framework for the 380 kV Marjan–Safaniyah HVAC transmission line by integrating Deep Learning with Physics-Informed Neural Networks (PINNs). The PINN model embeds fundamental electrical laws, such as Kirchhoff’s Current Law (KCL), directly into the learning process, thereby constraining predictions to physically plausible behaviors and enhancing robustness and accuracy. Developed in MATLAB/Simulink using the Deep Learning Toolbox, the proposed framework performs fault detection and fault type classification within a unified architecture. A comparative analysis demonstrates that the hybrid PINN approach significantly outperforms conventional Deep Learning models, particularly by reducing false negatives and improving class discrimination. Furthermore, this study highlights the crucial role of balanced and representative datasets in achieving a reliable performance. Validation through confusion matrices and KCL residual histograms confirms the enhanced physical consistency and predictive reliability of the model. Overall, the proposed framework provides a powerful and scalable solution for real-time monitoring, fault diagnosis, and intelligent decision-making in high-voltage power transmission systems. Full article

Accurate identification of equivalent thermal parameters (ETPs) is crucial for optimizing energy efficiency in residential buildings during winter electric heating. This study proposes a physics-informed neural network (PINN) approach to estimate ETP model parameters, integrating physical constraints with data-driven learning to enhance robustness. The method is validated using real-world measurements from seven rural residences, with indoor and outdoor temperatures and heating power sampled every 15 min. The PINN is compared with linear regression (LR), heuristic methods (GA, PSO, TROA), and data-driven methods (RF, XGBoost, LSTM). The results show that the PINN reduces MAE by over 90% compared to LR, 42% compared to heuristic methods, and 75% compared to pure data-driven methods, with similar improvements in RMSE and MAPE, while maintaining moderate computational time. This work highlights the potential of PINNs as an efficient and reliable tool for building energy management, offering a promising solution for parameter identification within the specific context of the studied residences, with future work needed to confirm scalability across diverse climates and building types. Full article

Data of operational conditions of structural components, acquired, e.g., in structural health monitoring (SHM), is of great interest to optimise products from one generation to the next, for example, by adapting them to occurring operational loads. To acquire data for this purpose in the desired quality, an optimal sensor placement for so-called shape and load sensing is required. In the case of large-scale structural components, wireless sensor networks (WSN) could be used to process and transmit the acquired data for real-time monitoring, which furthermore requires an optimisation of sensor node positions. Since most publications focus only on the optimal sensor placement or the optimisation of sensor node positions, a methodology for both is implemented in a Python tool, and an optimised WSN is realised on a demonstration part, loaded at a test bench. For this purpose, the modal method is applied for shape sensing as well as a physics-informed neural network for solving inverse problems in shape sensing (iPINN). The WSN is realised with strain gauges, HX711 analogue-digital (A/D) converters, and Arduino Nano 33 IoT microprocessors for data submission to a server, which allows real-time visualisation and data processing on a Python Flask server. The results demonstrate the applicability of the presented methodology and its implementation in the Python tool for achieving high-accuracy shape sensing with WSNs. Full article

In this paper, an intelligent simulation method for chloride ion diffusion behavior in marine concrete is established based on a physical information neural network. The dimensionless constraint equation is constructed to solve the influence of different physical parameter dimensions on the generalization ability of the model. The performance of the simulation method is verified by field measured data. The influence of different exposure ages and chloride ion diffusion coefficients on chloride ion diffusion behavior is quantified. The temporal and spatial distribution characteristics of chlorine ion (C) in concrete under a multi-dimensional diffusion state are analyzed, and the reliability model is further constructed to evaluate the degradation law of the service performance of marine concrete. The results show that the dimensionless physical information neural network model can effectively simulate the diffusion behavior and spatial–temporal distribution of C in marine concrete. The maximum error between the predicted value and the experimental value obtained by the method proposed in this paper is less than 15%. The dimension problem of high-order nonlinear equations can be solved by Non-PINN, with the maximum error value less than 5%. The spatial–temporal distributions of C on different exposed surfaces under a multi-dimensional diffusion state are independent of each other. The service performance of marine concrete will increase with an increase in slag content and protective layer thickness, and decrease with an increase in surface chloride ion concentration. Full article

Predicting tunnel seepage field is a critical challenge in the construction of underground engineering projects. While traditional analytical solutions and numerical methods struggle with complex geometric boundaries, standard Physics-Informed Neural Networks (PINNs) encounter additional challenges in tunnel seepage problems, including training instability, boundary handling difficulties, and low sampling efficiency. This paper develops an enhanced PINN framework designed specifically for predicting tunnel seepage field by integrating Exponential Moving Average (EMA) weight stabilization, Residual Adaptive Refinement with Distribution (RAR-D) sampling, and Bayesian optimization for collaborative training. The framework introduces a trial function method based on an approximate distance function (ADF) to address the precise handling of circular tunnel boundaries. The results demonstrate that the enhanced PINN framework achieves an exceptional prediction accuracy with an overall average relative error of 5 × 10⁻⁵. More importantly, the method demonstrates excellent practical applicability in data-scarce scenarios, maintaining acceptable prediction accuracy even when monitoring points are severely limited. Bayesian optimization reveals the critical insight that loss weight configuration is more important than network architecture in physics-constrained problems. This study is a systematic application of PINNs to prediction of tunnel seepage field and holds significant value for tunnel construction monitoring and risk assessment. Full article

Time series models are widely used to examine temporal dynamics and uncover patterns across diverse fields. A commonly employed approach for modeling such data is the (Vector) Autoregressive (AR/VAR) model, in which each variable is represented as a linear combination of its own and others’ lagged values. However, the traditional (V)AR framework relies on the key assumption of stationarity, that autoregressive coefficients remain constant over time, which is often violated in practice, especially in systems affected by structural breaks, seasonal fluctuations, or evolving causal mechanisms. To overcome this limitation, Time-Varying (Vector) Autoregressive (TV-AR/TV-VAR) models have been developed, enabling model parameters to evolve over time and thus better capturing non-stationary behavior. Conventional approaches to estimating such models, including generalized additive modeling and kernel smoothing techniques, often require strong assumptions about basis functions, which can restrict their flexibility and applicability. To address these challenges, we introduce a novel framework that leverages physics-informed neural networks (PINN) to model TV-AR/TV-VAR processes. The proposed method extends the PINN framework to time series analysis by reducing reliance on explicitly defined physical structures, thereby broadening its applicability. Its effectiveness is validated through simulations on synthetic data and an empirical study of real-world health-related time series. Full article

Physics-informed neural networks (PINNs) have emerged as a promising alternative to purely data-driven neural networks (NNs) for surrogate modeling, particularly in data-scarce scenarios. This study evaluates the performance of hybrid-PINNs against traditional NNs for modeling the adsorption step of a Direct Air Capture (DAC) process. As the complexity of the modeled system increases, larger datasets and longer computational times are required for numerical methods. Therefore, the study aims to develop approaches that minimize data requirements while maintaining accuracy, which is crucial for efficient modeling of complex physical systems. While both AI models can achieve high accuracy with abundant data, the advantages of hybrid-PINNs become more evident as data becomes scarce. In the intermediate and low-data regimes, the physics constraints embedded in hybrid-PINNs significantly improve generalization and predictive accuracy. For extreme low-data conditions, a curriculum learning strategy is implemented, progressively enforcing physics constraints to mitigate underfitting and enhance model stability. Despite these benefits, hybrid-PINNs exhibit a computational cost approximately one order of magnitude higher than traditional NNs as enforcing physics constraints increases training complexity. The results suggest that PINNs hold potential for modeling complex multi-physics problems in DAC and beyond, provided challenges related to gradient balancing and computational efficiency are addressed. Full article