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• A new framework based on the PINNs is presented for bimaterial interface crack analysis. • An enriched PINNs is proposed to correctly capture the local crack-tip behavior. • The complex SIFs of interfacial cracks can be directly calculated with very high accuracy. This study explores the application of physics-informed neural networks (PINNs) to analyze interface crack problems within the context of elastic bimaterial fracture mechanics. Bimaterial interface cracks exhibit a distinct behavior compared to cracks in homogeneous materials, and this behavior often involves oscillatory phenomena that can pose challenges in numerical modeling. By employing neural networks for solution approximation, PINNs are meshless and are trained using batches of collocation points, which may be randomly or strategically sampled across the computational domain. To effectively capture the oscillatory singular behavior in the crack-tip regions, this paper introduces an enhanced PINNs formulation that enables the modeling of interface cracks without requiring any refinement near the crack-tip. The trainable parameters of the current PINNs are dynamically optimized throughout the training process to fulfill both the underlying differential equations and the associated initial/boundary conditions. One of the significant advantages of the present PINNs is that it uses enrichment functions to capture the behavior around the crack region, allowing for greater flexibility in handling irregular or complex crack paths. The method's accuracy and stability are validated across several benchmark examples. [ABSTRACT FROM AUTHOR]

In the contemporary data-driven era, the fields of machine learning, deep learning, big data, statistics, and data science are essential for forecasting outcomes and getting insights from data. This paper looks at how machine learning approaches can be used to anticipate solar power generation, assess heat exchanger heat transfer efficiency, and predict the thermo-physical properties of nanofluids. The review specifically focuses on the potential use of machine learning in solar thermal applications, perovskites, and photovoltaic power forecasting. Predictions of nanofluid characteristics and device performance may be more accurately made with the development of machine learning algorithms. The use of machine learning in the creation of new perovskites and the assessment of their effectiveness and stability is also included in the review. Additionally, the paper explores developments in artificial intelligence, particularly deep learning, in this area and offers insights into techniques for forecasting solar power, including PV production, cloud motion, and weather classification. [ABSTRACT FROM AUTHOR]

In this paper, we construct two deep neural network (DNN) approaches based on the hybridized discontinuous Galerkin (HDG) method for solving some elliptic problems. The main idea is to use an HDG scheme for spatial discretization and then estimate solutions using the deep learning idea. In fact, by employing DNN, we can achieve robust methods compared to classical methods for solving noisy and high-dimensional problems. A brief analysis shows that the loss functions corresponding to the proposed methods, which are called DNN-HDG-I and DNN-HDG-II, converge to zero as the mesh step size reduces. By testing several examples in one, two, and three dimensions, we demonstrate the performance of the proposed methods that show their apparent advantages especially compared to classical HDG methods. As we expected, the DNN-HDG methods can efficiently and accurately extract the pattern of the solutions in all three dimensions. To show the superiority of the proposed schemes, the DNN-HDG methods are compared with the classical HDG method for solving a problem involving some noisy data. Specifically, we employ the proposed methods for solving a problem which its exact solution is not accessible and compare it with the HDG solution. In this paper, the uniformly random data and Jacobi polynomial roots are considered, respectively, as the training data on the boundary and quadrature points for approximating integrals. Also, we find that the proposed methods are not required a high number of neurons (at most 30) and hidden layers (at most 10) for satisfactory results with acceptable accuracy. [ABSTRACT FROM AUTHOR]

Moisture diffusion is a common phenomenon in geotechnical engineering, and its induced deformation seriously affects the stability of the engineering structure, such as embankment slope instability and tunnel surrounding rock deformation. Numerical simulation is an effective method for moisture diffusion-deformation coupling computation, but it has a large computational cost and a high learning threshold for ordinary engineers. In this paper, a surrogate model based on deep convolutional neural networks is presented for moisture diffusion-deformation coupling computation. First, designing the neural network structure includes the dense blocks and transition layers, and hyperparameters. Then, the moisture diffusion-deformation coupling model in the finite discrete element method (FDEM) software package MultiFracS is used to obtain the high-fidelity simulation data for the moisture diffusion-deformation examples. The simulation data and the key parameter (elastic modulus and Poisson's ratio) are processed into the image data structure (matrix) for training the surrogate model. Finally, the root means square error and the correlation coefficient are used to evaluate the effectiveness of the surrogate model. The results reveal that, rather than taking several hours to run a numerical model, the surrogate model only takes a few seconds to obtain the deformation and stress under a given moisture field and material parameters, which significantly improves prediction efficiency. Using this surrogate model, the engineers can obtain the deformation law just only modifying key parameters. Moreover, the surrogate model can be packaged into a mobile app to provide support for rapid decision-making on the project site. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new deep learning algorithm based on the physics-informed neural network (PINN) for solving the Cahn–Hilliard (CH) equations. We adopt the discrete time model of the PINN and use Runge–Kutta methods to discretize the time variable. We introduce a novel loss function and update it at each time step so that the computational cost can be significantly reduced compared to some existing methods. Numerical results of several one-dimensional and two-dimensional CH equations are presented to validate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Thin-walled structural problems have been a longstanding computational challenge. The research bottleneck in applying the standard numerical methods for such problems arises from their special geometrical configurations in which the thickness-to-length ratio of the thin-structures is usually up to the order of 10−6 or even smaller. In this paper, we present a method to solve such problems using physics-informed neural networks (PINNs) which are trained to satisfy the differential operator and the corresponding boundary/initial conditions. The PINNs-based method is meshless which is a key feature since mesh-based methods become infeasible for problems with ultra-thin shapes. Instead of using a mesh, the PINNs are trained on batches of randomly sampled collocation points. The algorithm is tested for a class of thin-walled structural problems, including elastic/piezoelectric thin-films as well as ultra-thin coating/substrate structures. We also present comparisons with numerical solutions obtained by using an advanced boundary element method (BEM). Accurate and reliable PINNs results can be achieved for a relative thickness-to-length ratio of the thin structures as small as 10−8, which is sufficient for modeling most of thin structures as used in smart materials. A self-contained MATLAB code and data-sets accompanying this paper are also provided. [ABSTRACT FROM AUTHOR]

Nowadays, Deep Learning is drastically revolutionizing financial research as well as industry. Many methods have been discussed in the last few years, mainly related to option pricing. In fact, traditional approaches such as Monte Carlo simulation or finite difference methods are seriously harmed by multi-dimensional underlying and path dependency. Thus, dealing with particular contracts such as American multi-asset options is still rough. This paper addresses such a problem by pricing said put options with a novel meshless methodology, named Physics-Informed Neural Networks (PINNs), based on Artificial Intelligence. PINN paradigm has been recently introduced in Deep Learning literature. It exploits the theoretical background of the universal approximation theorem for neural networks to solve Partial Differential Equations numerically. This Deep Learning meshless method incorporates the equation and its initial and boundary conditions thanks to a specially designed loss function. We develop a suitable PINN for the proposed problem by introducing an algorithmic trick for improving the convergence of the free boundary problem. Furthermore, the worthiness of the proposal is assessed by several experiments concerned with single and multi-asset options. Finally, a parametric model is built to benefit further studies of option value behaviour related to particular market conditions. [ABSTRACT FROM AUTHOR]

Influences of a helical absorber tube on the thermal performances of a double-fluid parabolic trough solar collector (PTSC) occupied by non-Newtonian nanofluid are investigated numerically. The problem geometry includes a double-fluid parabolic trough solar receiver with high insulation and a non-circular adsorbent tube. The finite volume method, SIMPLE algorithm, and k-ε model were used for numerical solutions. The result showed that the double-fluid solar receiver was equipped with a helical absorber tube filled with nanofluid with a volume fraction of 4% and nanoparticles diameter of 50nm flowing in the absorber tube, and an annulus glass cover is introduced as the optimal model in this paper. For single-flow PTSC, the value of η max nanofluid- and water-based PTSCs are 47.5% and 43.1%, respectively, at a flow velocity of Re=5000. In double-flow PTSC, the value of η max at 1 and 4 vol.% is 56.5% and 58.2%, respectively, at the flow velocity of Re=5000. Finally, a deep learning method is employed to examine the parameters affecting the efficiency, including the concentration and diameter of nanoparticles and Re number. The results indicate the ANN has acceptable performance in prediction of the efficiency of the double-fluid parabolic trough solar collector occupied by non-Newtonian nanofluid. [ABSTRACT FROM AUTHOR]