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The rapid development of urbanization has led to a continuous rise in number of elevators. This has led to elevator failures from time to time. At present, although there are some studies on elevator fault diagnosis, they are more or less limited by the lack of data to make the research more superficial. For such complex special equipment as elevator, it is difficult to obtain reliable and sufficient data to train the fault diagnosis model. To address this issue, this paper first establishes a numerical model of vertical vibration for elevators with three degrees of freedom. The obtained motion equations are then used as constraints to acquire simulated vibration data through PINNs. Next, the proposed e-RGCN is employed for elevator fault diagnosis. Finally, experimental validation shows that the fault diagnosis accuracy with the participation of digital twins exceeds 90%, and the accuracy of the proposed model reaches 96.61%, significantly higher than that of other comparative models.

This research aims to study and assess state-of-the-art physics-informed neural networks (PINNs) from different researchers’ perspectives. The PRISMA framework was used for a systematic literature review, and 120 research articles from the computational sciences and engineering domain were specifically classified through a well-defined keyword search in Scopus and Web of Science databases. Through bibliometric analyses, we have identified journal sources with the most publications, authors with high citations, and countries with many publications on PINNs. Some newly improved techniques developed to enhance PINN performance and reduce high training costs and slowness, among other limitations, have been highlighted. Different approaches have been introduced to overcome the limitations of PINNs. In this review, we categorized the newly proposed PINN methods into Extended PINNs, Hybrid PINNs, and Minimized Loss techniques. Various potential future research directions are outlined based on the limitations of the proposed solutions.

Modeling coupled groundwater flow and reactive transport for multi‐query tasks is computationally prohibitive, and standard Physics‐Informed Neural Networks (PINNs) require costly retraining for each new parameter. We introduce the Multi‐Physics Generative Pre‐trained PINN (MP‐GPT‐PINN), a meta‐learning framework to resolve this bottleneck. Its innovation is a two‐stage strategy: an offline pre‐training stage uses a greedy algorithm to build a compact library of PINN solutions for key parameters. A rapid online stage then generates new solutions by combining these pre‐trained bases in an optimal linear manner. For multi‐physics problems, we designed a parallel dual‐network architecture to couple the seepage and chemical fields robustly. Validated across complex groundwater systems, MP‐GPT‐PINN accelerates online predictions by four orders of magnitude while maintaining high fidelity, with dimensionless L2${L}_{2}$relative errors for physical fields approaching 10−3. This efficiency breakthrough makes computationally intensive tasks, such as large‐scale parameter inversion and uncertainty quantification, feasible in geosciences.

Physics‐informed neural networks (PINNs) are gaining attention as an alternative approach to solve scientific problems governed by differential equations. This work aims at assessing the effectiveness of PINNs to solve a set of partial differential equations for which this method has never been considered, namely the augmented shallow water equations (SWEs) with topography. Differently from traditional SWEs, the bed elevation is considered as an additional conserved variable, and therefore one more equation expressing the fixed‐bed condition is included in the system. This approach allows the PINN model to leverage automatic differentiation to compute the bed slopes by learning the topographical information during training. PINNs are here tested for different one‐dimensional cases with non‐flat topography, and results are compared with analytical solutions. Though some limitations can be highlighted, PINNs show a good accuracy for the depth and velocity predictions even in the presence of non‐horizontal bottom. The solution of the augmented system of SWEs can therefore be regarded as a suitable alternative strategy to deal with flows over complex topography using PINNs, also in view of future extensions to realistic problems. Key Points Physics‐informed neural networks (PINNs) are applied to solve the augmented shallow water equations with topography Applications to one‐dimensional cases of free‐surface flows over non‐flat bottom show a good solution accuracy Solving the augmented system is an alternative way to deal with non‐flat topography

The modeling of cross-ply composite laminates using numerical methods has been a difficult task, leading to the development of various finite element method and other analytical solutions. However, as materials science advances, this problem has become more complex, presenting new challenges that require reliable and novel approaches. In this study, we propose the utilization of machine learning, specifically physics informed neural networks (PINN), for the first time to examine the behavior of composite plate. By solving a system of partial differential equations derived from the virtual work equilibrium principle, PINN are employed as a method to solve these equations using a generalized strong-form approach. To address the issue of imbalanced loss functions, we also propose adjusting the loss function in this research. Once trained, PINN serve as a surrogate model capable of predicting displacements and stresses in cross-ply composite laminates. To demonstrate the effectiveness and reliability of PINN, we investigate two examples of laminates with different material distributions and boundary conditions including boundary conditions on displacement and boundary conditions on stress, comparing the results with the benchmark Navier solution. The research and obtained results showcase the performance and accuracy of PINN, highlighting their potential as a surrogate model for solving problems related to cross-ply composite laminates.

AI for PDEs has garnered significant attention, particularly physics‐informed neural networks (PINNs). However, PINNs are typically limited to solving specific problems, and any changes in problem conditions necessitate retraining. Therefore, we explore the generalization capability of transfer learning in the strong and energy forms of PINNs across different boundary conditions, materials, and geometries. The transfer learning methods we employ include full finetuning, lightweight finetuning, and low‐rank adaptation (LoRA). Numerical experiments include the Taylor‐Green Vortex in fluid mechanics and functionally graded materials with elastic properties, as well as a square plate with a circular hole in solid mechanics. The results demonstrate that full finetuning and LoRA can significantly improve convergence speed while providing a slight enhancement in accuracy. However, the overall performance of lightweight finetuning is suboptimal, as its accuracy and convergence speed are inferior to those of full finetuning and LoRA.

Data scarcity is a major challenge when training deep learning (DL) models. DL demands a large amount of data to achieve exceptional performance. Unfortunately, many applications have small or inadequate data to train DL frameworks. Usually, manual labeling is needed to provide labeled data, which typically involves human annotators with a vast background of knowledge. This annotation process is costly, time-consuming, and error-prone. Usually, every DL framework is fed by a significant amount of labeled data to automatically learn representations. Ultimately, a larger amount of data would generate a better DL model and its performance is also application dependent. This issue is the main barrier for many applications dismissing the use of DL. Having sufficient data is the first step toward any successful and trustworthy DL application. This paper presents a holistic survey on state-of-the-art techniques to deal with training DL models to overcome three challenges including small, imbalanced datasets, and lack of generalization. This survey starts by listing the learning techniques. Next, the types of DL architectures are introduced. After that, state-of-the-art solutions to address the issue of lack of training data are listed, such as Transfer Learning (TL), Self-Supervised Learning (SSL), Generative Adversarial Networks (GANs), Model Architecture (MA), Physics-Informed Neural Network (PINN), and Deep Synthetic Minority Oversampling Technique (DeepSMOTE). Then, these solutions were followed by some related tips about data acquisition needed prior to training purposes, as well as recommendations for ensuring the trustworthiness of the training dataset. The survey ends with a list of applications that suffer from data scarcity, several alternatives are proposed in order to generate more data in each application including Electromagnetic Imaging (EMI), Civil Structural Health Monitoring, Medical imaging, Meteorology, Wireless Communications, Fluid Mechanics, Microelectromechanical system, and Cybersecurity. To the best of the authors’ knowledge, this is the first review that offers a comprehensive overview on strategies to tackle data scarcity in DL.

The solving of the derivative nonlinear Schrödinger equation (DNLS) has attracted considerable attention in theoretical analysis and physical applications. Based on the physics-informed neural network (PINN) which has been put forward to uncover dynamical behaviors of nonlinear partial different equation from spatiotemporal data directly, an improved PINN method with neuron-wise locally adaptive activation function is presented to derive localized wave solutions of the DNLS in complex space. In order to compare the performance of above two methods, we reveal the dynamical behaviors and error analysis for localized wave solutions which include one-rational soliton solution, genuine rational soliton solutions and rogue wave solution of the DNLS by employing two methods, and also exhibit vivid diagrams and detailed analysis. The numerical results demonstrate the improved method has faster convergence and better simulation effect. On the basis of the improved method, the effects for different numbers of initial points sampled, residual collocation points sampled, network layers, neurons per hidden layer on the second-order genuine rational soliton solution dynamics of the DNLS are considered, and the relevant analysis when the locally adaptive activation function chooses different initial values of scalable parameters is also exhibited in the simulation of the two-order rogue wave solution.

In order to offer guidelines for physics-informed neural network (PINN) implementation, this study presents a comprehensive review of PINN, an emerging field at the intersection of deep learning and computational physics. PINN offers a novel approach to solve physics problems by leveraging the flexibility and scalability of neural networks, even with small or no data. First, a general description of different physics problem types and target tasks addressable with PINN was provided. A generic PINN architecture was described in detail using a component-wise approach, with components ranging from collocation points to optimization methods. Then, we surveyed studies that sought to improve upon each of these components. To offer practical insights, we highlighted studies that focused on key issues of PINN implementation and showcased three practical applications. Lastly, a summary and potential research directions were provided to offer guidelines for reliable and customized PINN implementations.

The modeling and simulation of polymer systems present unique challenges due to their intrinsic complexity and multi-scale behavior. Traditional computational methods, while effective, often struggle to balance accuracy with computational efficiency, especially when bridging the atomistic to macroscopic scales. Recently, physics-informed neural networks (PINNs) have emerged as a promising tool that integrates data-driven learning with the governing physical laws of the system. This review discusses the development and application of PINNs in the context of polymer science. It summarizes the recent advances, outlines the key methodologies, and analyzes the benefits and limitations of using PINNs for polymer property prediction, structural design, and process optimization. Finally, it identifies the current challenges and future research directions to further leverage PINNs for advanced polymer modeling.