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Due to the development of high performance computing, deep learning algorithm has made a significant progress in many fields such as computational mathematics. The physics-informed neural networks have put forward a innovative idea for tackling a broad range of forward and inverse problems of partial differential equations. Motivated by the philosophy of physics-informed neural network and the multigrid method, we introduce the gradient information of numerical solution of physics-informed neural network into the new neural networks and propose the rectified-physics informed neural network for solving stationary partial differential equations. And for solving multi-objective optimization of neural networks, the dynamic weight strategy is adopted to balance numerical difference among terms in the loss function, and effectively alleviate the gradient ill-conditioned phenomenon. Finally, we perform a series of numerical experiments to demonstrate effectiveness of the RPINNs method which is combined with the dynamic weight strategy to improve calculation accuracy. • RPINNs based on multi-grid are proposed to solve the stationary PDEs. • RPINNs are improved by the dynamic weight strategy. • Incorporate the dynamic weight strategy based on NTK to RPINNs. • Study efficiency of calculating gradients by automatic differentiation and finite difference. [ABSTRACT FROM AUTHOR]

In this work, we propose an effective and efficient cross-scenario glasses retrieval model with the goal of providing a new online shopping experience. Two challenging issues arise for cross-scenario glasses retrieval: identifying glasses in a query image and extracting features from the identified glasses. To properly address these issues, we introduce a novel segmentation-free framework which includes a glasses detection model, an attribute recognition model, and a coarse-to-fine search strategy. Specifically, a new keypoint-based scheme called EyeGlasses keYPoinT (EGYPT) for glasses detection is proposed, in which a set of representative keypoints along a glasses frame are automatically identified. Based on these detected keypoints, various local feature descriptors are extracted to learn the semantic attributes of the glasses. Furthermore, fast retrieval is achieved by applying a hierarchical search strategy based on the index of the attributes. An experimental analysis with real-world photos and product images verifies the efficacy and efficiency of our proposed retrieval model. [ABSTRACT FROM AUTHOR]

Earthquake prevention is of fundamental interest in seismic research area. Seismic metamaterials proved very useful for this purpose, but because they are mainly based on resonant structures, the working frequency bandwidth of these metamaterials is narrow. This work aims to increase the bandwidth by improving cylindrical resonant structure. Two types of cylindrical structures with four petals attached to the four sides of hollow and solid cylinders are proposed. Their bandgap properties have been investigated by using the finite element method. Particularly, considering more realistic site conditions for seismic surface wave propagation, we explored the properties of the proposed structures for horizontally stratified soils, besides homogeneous soil. The results show that a low-frequency wide bandgap is provided in case of homogeneous soil. Excitedly, in case of a stratified substrate, an additional bandgap is obtained in lower frequency region. Moreover, to confirm the feasibility of the proposed structures, the transmission coefficients for the finite unit cells are calculated for both homogeneous and horizontally stratified soils along with the different directions. The finding substantiates that the finite system for stratified soils can effectively attenuate seismic surface waves within the two low-frequency bandgaps occupying the relative bandwidths of 154% and 81%. • Petal-shaped cylindrical model on both homogeneous and stratified soil, combined with PML is proposed. • Finite element method is being used to investigate bandgap properties. • Low-frequency bandgaps occupying the relative bandwidths of 154% and 81% are achieved. • The influences of material and geometrical parameters on the surface-wave attenuation zone are investigated. [ABSTRACT FROM AUTHOR]