Junpu Li

This study proposes a boundary integral-enhanced physics-informed neural network (BIE-PINN) for solving nonlinear partial differential equations. BIE-PINN decomposes the nonlinear equation into a linear part and a nonlinear source term, where the latter is treated as a generalized source and predicted by the current neural network. A boundary integral loss derived from the linear operator of the equation is incorporated into the total loss function as a strong spatial constraint. For transient problems, a Runge-Kutta loss is introduced as a strong temporal constraint. By suppressing the accumulation and propagation of local errors over time, this loss effectively confines perturbations near sharp fronts and prevents them from polluting the entire domain, thereby enhancing long-term accuracy and stability. In addition, a staged learning rate annealing algorithm is designed to adaptively balance the weights of different loss terms across training phases. Furthermore, activation functions based on fundamental solutions are introduced to improve generalization. Numerical experiments show that compared with PINN, BIE-PINN not only achieves comparable accuracy using only 6% of the collocation points and 44.7% of the training time, but also accurately recovers unknown parameters in severely ill-posed inverse problems even when the data is extremely sparse and the boundary conditions are incomplete.

Diamond-like carbon (DLC) has attracted much attention due to its unique properties such as high chemical inertness, optical transparency, and high biocompatibility. In this study, the total gas flow rate was kept constant, while the ratio of reactive gases was varied to deposit nitrogen-doped diamond-like carbon thin films on glass substrates using radiofrequency plasma-enhanced chemical vapor deposition. The effects of the gas flow ratio on the composition, microstructure, surface morphology, and optical properties of the thin films were investigated through extended deposition times. It was found that with an increase in the nitrogen-to-methane gas flow ratio, the film surface became smoother and more compact. The maximum transmittance in the visible range reached 90%, and the highest and lowest transmittance in the same ultraviolet wavelength region differed by up to 25.62% among several sample groups. The optical bandgap decreased from 3.58 eV to 3.46 eV, contrary to the trend of the sp² fraction variation. Compared with other studies, this study considered the preparation of nitrogen-doped diamondoids using a chemical vapor deposition method with a lesser total gas flow rate passed into it, which provides practical data reference value for the preparation of N-DLC.

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Advances in Applied Mathematics and Mechanics (AAMM) publishes as rapidly as possible manuscripts of high standard, through electronic submission and reviewing. It provides a fast communication platform among researchers using mathematics as a tool for solving problems in mechanics, with particular emphasis in the integration of theory and applications. The mathematical tools used to solve problems in mechanics include analytical, semi-analytical, numerical and artificial intelligence ones. In order to cover as wide an audience as possible, abstract or axiomatic mathematics is not encouraged. As an international journal, AAMM is published in a timely fashion in printed and electronic forms.