Boundary integrated neural networks (BINNs) for acoustic radiation and scattering

This paper presents a novel approach called the boundary integrated neural networks (BINNs) for analyzing acoustic radiation and scattering. The method introduces fundamental solutions of the time-harmonic wave equation to encode the boundary integral equations (BIEs) within the neural networks, replacing the conventional use of the governing equation in physics-informed neural networks (PINNs). This approach offers several advantages. Firstly, the input data for the neural networks in the BINNs only require the coordinates of "boundary" collocation points, making it highly suitable for analyzing acoustic fields in unbounded domains. Secondly, the loss function of the BINNs is not a composite form, and has a fast convergence. Thirdly, the BINNs achieve comparable precision to the PINNs using fewer collocation points and hidden layers/neurons. Finally, the semi-analytic characteristic of the BIEs contributes to the higher precision of the BINNs. Numerical examples are presented to demonstrate the performance of the proposed method

Boundary integrated neural networks (BINNs) for 2D elastostatic and piezoelectric problems: Theory and MATLAB code

In this paper, we make the first attempt to apply the boundary integrated neural networks (BINNs) for the numerical solution of two-dimensional (2D) elastostatic and piezoelectric problems. BINNs combine artificial neural networks with the well-established boundary integral equations (BIEs) to effectively solve partial differential equations (PDEs). The BIEs are utilized to map all the unknowns onto the boundary, after which these unknowns are approximated using artificial neural networks and resolved via a training process. In contrast to traditional neural network-based methods, the current BINNs offer several distinct advantages. First, by embedding BIEs into the learning procedure, BINNs only need to discretize the boundary of the solution domain, which can lead to a faster and more stable learning process (only the boundary conditions need to be fitted during the training). Second, the differential operator with respect to the PDEs is substituted by an integral operator, which effectively eliminates the need for additional differentiation of the neural networks (high-order derivatives of neural networks may lead to instability in learning). Third, the loss function of the BINNs only contains the residuals of the BIEs, as all the boundary conditions have been inherently incorporated within the formulation. Therefore, there is no necessity for employing any weighing functions, which are commonly used in traditional methods to balance the gradients among different objective functions. Moreover, BINNs possess the ability to tackle PDEs in unbounded domains since the integral representation remains valid for both bounded and unbounded domains. Extensive numerical experiments show that BINNs are much easier to train and usually give more accurate learning solutions as compared to traditional neural network-based methods

Evaluation and optimisation of micro flexible rolling process parameters by orthogonal trial design

As the strip thickness is in the range of sub-millimetre in micro flexible rolling, springback ratio in thickness direction has a significant impact on product quality, which is influenced by various process parameters during forming process. This paper focuses on performing a numerical and experimental investigation to evaluate the effects of initial strip thickness, friction coefficient and rolling speed on the springback ratio in thickness direction during the micro flexible rolling process with reductions of 20 to 50% using orthogonal trial design, and wherein the three-level factors orthogonal array is chosen and nine representative orthogonal trials for each reduction have been implemented. With the significance of each process parameter for each reduction identified by variance analysis, an optimum proposal for each reduction to obtain the minimum springback ratio has been determined numerically, which is afterwards confirmed by experimental data. Moreover, a qualitative estimate of the influences of process parameters on the rolling force, as well as a quantitative analysis of the relationship between the length of thickness transition zone and the parameter level have also been carried out with reference to the obtained results

A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions

In this work, a hybrid localized meshless method is developed for solving transient groundwater flow in two dimensions by combining the Crank–Nicolson scheme and the generalized finite difference method (GFDM). As the first step, the temporal discretization of the transient groundwater flow equation is based on the Crank–Nicolson scheme. A boundary value problem in space with the Dirichlet or mixed boundary condition is then formed at each time node, which is simulated by introducing the GFDM. The proposed algorithm is truly meshless and easy to program. Four linear or nonlinear numerical examples, including ones with complicated geometry domains, are provided to verify the performance of the developed approach, and the results illustrate the good accuracy and convergency of the method

Depth-resolved enhanced spectral-domain OCT imaging of live mammalian embryos using gold nanoparticles as contrast agent

High‐resolution and real‐time visualization of the morphological changes during embryonic development are critical for studying congenital anomalies. Optical coherence tomography (OCT) has been used to investigate the process of embryogenesis. However, the structural visibility of the embryo is decreased with the depth due to signal roll‐off and high light scattering. To overcome these obstacles, in this study, combined is a spectral‐domain OCT (SD‐OCT) with gold nanorods (GNRs) for 2D/3D imaging of live mouse embryos. Inductively coupled plasma mass spectrometry is used to confirm that GNRs can be effectively delivered to the embryos during ex vivo culture. OCT signal, image contrast, and penetration depth are all enhanced on the embryos with GNRs. These results show that after GNR treatment, more accurate spatial localization and better contrasting of the borders among organs can be observed on E9.5 and E10.5 mouse embryos. Furthermore, the strong optical absorbance of GNRs results in much clearer 3D images of the embryos, which can be used for calculating the heart areas and volumes of E9.5 and E10.5 embryos. These findings provide a promising strategy for monitoring organ development and detecting congenital structural abnormalities in mice