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This study aims to explore the evolving field of physics-informed neural networks (PINNs) through an analysis of 996 records retrieved from the Web of Science (WoS) database from 2019 to 2022.

WoS database was analyzed for PINNs using an inhouse python code. The author’s collaborations, most contributing institutes, countries and journals were identified. The trends and application categories were also analyzed.

The papers were classified into seven key domains: Fluid Dynamics and computational fluid dynamics (CFD); Mechanics and Material Science; Electromagnetism and Wave Propagation; Biomedical Engineering and Biophysics; Quantum Mechanics and Physics; Renewable Energy and Power Systems; and Astrophysics and Cosmology. Fluid Dynamics and CFD emerged as the primary focus, accounting for 69.3% of total publications and witnessing exponential growth from 22 papers in 2019 to 366 in 2022. Mechanics and Material Science followed, with an impressive growth trajectory from 3 to 65 papers within the same period. The study also underscored the rising interest in PINNs across diverse fields such as Biomedical Engineering and Biophysics, and Renewable Energy and Power Systems. Furthermore, the focus of the most active countries within each application category was examined, revealing, for instance, the USA’s significant contribution to Fluid Dynamics and CFD with 319 papers and to Mechanics and Material Science with 66 papers.

This analysis illuminates the rapidly expanding role of PINNs in tackling complex scientific problems and highlights its potential for future research across diverse domains.

Current methods for flow field reconstruction mainly rely on data-driven algorithms which require an immense amount of experimental or field-measured data. Physics-informed neural network (PINN), which was proposed to encode physical laws into neural networks, is a less data-demanding approach for flow field reconstruction. However, when the fluid physics is complex, it is tricky to obtain accurate solutions under the PINN framework. This study aims to propose a physics-based data-driven approach for time-averaged flow field reconstruction which can overcome the hurdles of the above methods.

A multifidelity strategy leveraging PINN and a nonlinear information fusion (NIF) algorithm is proposed. Plentiful low-fidelity data are generated from the predictions of a PINN which is constructed purely using Reynold-averaged Navier–Stokes equations, while sparse high-fidelity data are obtained by field or experimental measurements. The NIF algorithm is performed to elicit a multifidelity model, which blends the nonlinear cross-correlation information between low- and high-fidelity data.

Two experimental cases are used to verify the capability and efficacy of the proposed strategy through comparison with other widely used strategies. It is revealed that the missing flow information within the whole computational domain can be favorably recovered by the proposed multifidelity strategy with use of sparse measurement/experimental data. The elicited multifidelity model inherits the underlying physics inherent in low-fidelity PINN predictions and rectifies the low-fidelity predictions over the whole computational domain. The proposed strategy is much superior to other contrastive strategies in terms of the accuracy of reconstruction.

In this study, a physics-informed data-driven strategy for time-averaged flow field reconstruction is proposed which extends the applicability of the PINN framework. In addition, embedding physical laws when training the multifidelity model leads to less data demand for model development compared to purely data-driven methods for flow field reconstruction.

Physics-informed neural networks (PINNs) have become a new tendency in flow simulation, because of their self-advantage of integrating both physical and monitored information of fields in solving the Navier–Stokes equation and its variants. In view of the strengths of PINN, this study aims to investigate the impact of spatially embedded data distribution on the flow field results around the train in the crosswind environment reconstructed by PINN.

PINN can integrate data residuals with physical residuals into the loss function to train its parameters, allowing it to approximate the solution of the governing equations. In addition, with the aid of labelled training data, PINN can also incorporate the real site information of the flow field in model training. In light of this, the PINN model is adopted to reconstruct a two-dimensional time-averaged flow field around a train under crosswinds in the spatial domain with the aid of sparse flow field data, and the prediction results are compared with the reference results obtained from numerical modelling.

The prediction results from PINN results demonstrated a low discrepancy with those obtained from numerical simulations. The results of this study indicate that a threshold of the spatial embedded data density exists, in both the near wall and far wall areas on the train’s leeward side, as well as the near train surface area. In other words, a negative effect on the PINN reconstruction accuracy will emerge if the spatial embedded data density exceeds or slips below the threshold. Also, the optimum arrangement of the spatial embedded data in reconstructing the flow field of the train in crosswinds is obtained in this work.

In this work, a strategy of reconstructing the time-averaged flow field of the train under crosswind conditions is proposed based on the physics-informed data-driven method, which enhances the scope of neural network applications. In addition, for the flow field reconstruction, the effect of spatial embedded data arrangement in PINN is compared to improve its accuracy.

Pores are the primary cause of fatigue failure in laser-directed energy deposition (L-DED) titanium alloys, which are largely determined by their location, size and shape. It is crucial for promoting the application of L-DED titanium alloys and ensuring their safety that establishing a fatigue life prediction method induced by pores, resulting in a proposed fatigue life prediction framework for L-DED Ti-6Al-4V based on a physics-informed neural network (PINN) algorithm.

In this study, a novel fatigue life prediction framework for L-DED Ti-6Al-4V based on a PINN algorithm was proposed. The influence patterns of various fatigue-sensitive parameters were revealed. The paper also included validation and analysis of the method, such as hyperparameter analysis of the PINN, efficacy analysis driven by physical information and comparative analysis of different methods.

The proposed method demonstrated high accuracy, with a correlation coefficient of 0.99 with experimental life. The coefficient of determination was 0.95 and the mean squared error was 0.06.

The results indicate that the proposed fatigue life prediction framework was of strong generalization capability and robustness.

Accurately estimating the severity of derailment is a crucial step in quantifying train derailment consequences and, thereby, mitigating its impacts. The purpose of this paper is to propose a simplified approach aimed at addressing this research gap by developing a physics-informed 1-D model. The model is used to simulate train dynamics through a time-stepping algorithm, incorporating derailment data after the point of derailment.

In this study, a simplified approach is adopted that applies a 1-D kinematic analysis with data obtained from various derailments. These include the length and weight of the rail cars behind the point of derailment, the train braking effects, derailment blockage forces, the grade of the track and the train rolling and aerodynamic resistance. Since train braking/blockage effects and derailment blockage forces are not always available for historical or potential train derailment, it is also necessary to fit the historical data and find optimal parameters to estimate these two variables. Using these fitted parameters, a detailed comparison can be performed between the physics-informed 1-D model and previous statistical models to predict the derailment severity.

The results show that the proposed model outperforms the Truncated Geometric model (the latest statistical model used in prior research) in estimating derailment severity. The proposed model contributes to the understanding and prevention of train derailments and hazmat release consequences, offering improved accuracy for certain scenarios and train types

This paper presents a simplified physics-informed 1-D model, which could help understand the derailment mechanism and, thus, is expected to estimate train derailment severity more accurately for certain scenarios and train types compared with the latest statistical model. The performance of the braking response and the 1-D model is verified by comparing known ride-down profiles with estimated ones. This validation process ensures that both the braking response and the 1-D model accurately represent the expected behavior.

The purpose of this study is to solve the Reynolds equation for finite journal bearings by using the physics-informed neural networks (PINNs) method. As a meshless method, it is unnecessary to use big data to train the neural networks, but to satisfy the Reynolds equation and the corresponding boundary conditions by using the known physics information.

Here, the boundary conditions are enforced through the loss function firstly, i.e. the soft constrain method. After this, an equation was constructed to build a surrogate model for satisfying the corresponding boundary conditions naturally, i.e. the hard constrain method.

For the soft one, in brief, the pressure results agree well with existing results, apart from the ones on the boundaries. While for the hard one, it can be noted that the discrepancies on the boundaries are reduced significantly.

The PINNs method is used to solve the Reynolds equation for finite journal bearings, and the error values on the boundaries for the results of the soft constrain method are improved by using the hard constrain method. Therefore, the hard constraint maybe also a good option when the pressure results on the boundaries are emphasized.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-02-2023-0045/

The purpose of this paper is to develop surrogate models, using deep learning (DL), that can facilitate the application of EM analysis software. In the current status quo, electrical systems can be found in an ever-increasing range of products that are part of everyone’s daily live. With the advances in technology, industries such as the automotive, communications and medical devices have been disrupted with new electrical and electronic systems. The innovation and development of such systems with increasing complexity over time has been supported by the increased use of electromagnetic (EM) analysis software. Such software enables engineers to virtually design, analyze and optimize EM systems without the need for building physical prototypes, thus helping to shorten the development cycles and consequently cut costs.

The industry standard for simulating EM problems is using either the finite difference method or the finite element method (FEM). Optimization of the design process using such methods requires significant computational resources and time. With the emergence of artificial intelligence, along with specialized tools for automatic differentiation, the use of DL has become computationally much more efficient and cheaper. These advances in machine learning have ushered in a new era in EM simulations where engineers can compute results much faster while maintaining a certain level of accuracy.

This paper proposed two different models that can compute the magnetic field distribution in EM systems. The first model is based on a recurrent neural network, which is trained through a data-driven supervised learning method. The second model is an extension to the first with the incorporation of additional physics-based information to the authors’ model. Such a DL model, which is constrained by the laws of physics, is known as a physics-informed neural network. The solutions when compared with the ground truth, computed using FEM, show promising accuracy for the authors’ DL models while reducing the computation time and resources required, as compared to previous implementations in the literature.

The paper proposes a neural network architecture and is trained with two different learning methodologies, namely, supervised and physics-based. The working of the network along with the different learning methodologies is validated over several EM problems with varying levels of complexity. Furthermore, a comparative study is performed regarding performance accuracy and computational cost to establish the efficacy of different architectures and learning methodologies.

This study aims to explore the influence of Fourier-feature enhanced physics-informed neural networks (PINNs) on effectively solving two-dimensional local time-fractional anomalous diffusion equations with nonlinear thermal diffusivity. By tackling the shortcomings of conventional numerical methods in managing fractional derivatives and nonlinearities, this research addresses a significant gap in the literature regarding efficient solution strategies for complex diffusion processes.

This study uses a quantitative methodology featuring a feed-forward neural network architecture combined with a Fourier feature layer. Automatic differentiation is implemented to ensure precise gradient calculations for fractional derivatives. The effectiveness of the proposed approach is showcased through numerical simulations across various sub-diffusion and super-diffusion scenarios, with fractal space parameters adjusted to examine behavior. In addition, the training process is assessed using the Fisher information matrix to analyze the loss landscape.

The results demonstrate that the Fourier-feature enhanced PINNs effectively capture the dynamics of the anomalous diffusion equation, achieving greater solution accuracy than traditional methods. The analysis using the Fisher information matrix underscores the importance of hyperparameter tuning in optimizing network performance. These findings support the hypothesis that Fourier features improve the model’s capacity to represent complex solution behaviors, providing the relationship between model architecture and diffusion dynamics.

This research presents a novel approach to solving fractional anomalous diffusion equations through Fourier-feature enhanced PINNs. The results contribute to the advancement of computational methods in areas such as thermal engineering, materials science and biological diffusion modeling, while also providing a foundation for future investigations into training dynamics within neural networks.

This paper presents an original approach for learning models, partially known, of particular interest when performing source identification or structural health monitoring. The proposed procedures employ some amount of knowledge on the system under scrutiny as well as a limited amount of data efficiently assimilated.

Two different formulations are explored. The first, based on the use of informed neural networks, leverages data collected at specific locations and times to determine the unknown source term of a parabolic partial differential equation. The second procedure, more challenging, involves learning the unknown model from a single measured field history, enabling the localization of a region where material properties differ.

Both procedures assume some kind of sparsity, either in the source distribution or in the region where physical properties differ. This paper proposed two different neural approaches able to learn models in order to perform efficient inverse analyses.

Two original methodologies are explored to identify hidden property that can be recovered with the right usage of data. Both methodologies are based on neural network architecture.

By seamlessly integrating physical laws, physics-informed neural networks (PINNs) have flexibly solved a wide variety of partial differential equations (PDEs). However, encoding PDEs and constraints as soft penalties in the loss function can cause gradient imbalances, leading to training and accuracy issues. This study aims to introduce the augmented Lagrangian method (ALM) and transfer learning to address these challenges and enhance the effectiveness of PINNs for hydrodynamic lubrication analysis.

The loss function was reformatted by ALM, adaptively adjusting the loss weights during training. Transfer learning was used to accelerate the convergence of PINNs under similar conditions. Additionally, the iterative process for load balancing was reframed as an inverse problem by extending film thickness as a trainable variable.

ALM-PINNs significantly reduced the maximum absolute boundary error by almost 80%. Transfer learning accelerated PINNs for solving the Reynolds equation, reducing training epochs by an order of magnitude. The iterative process for load balancing was effectively eliminated by extending the thickness as a trainable parameter, achieving a maximum percentage error of 2.31%. These outcomes demonstrated strong agreement with FDM results, analytical solutions and experimental data.

This study proposes a PINN-based approach for hydrodynamic lubrication analysis that significantly improves boundary accuracy and the training process. Additionally, it effectively replaces the load balancing procedure. This methodology demonstrates considerable potential for broader applications across various boundary value problems and iterative processes.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2024-0277/