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The accuracy of information transmission while solving domain decomposed problems is crucial to smooth transition of a solution around the interface/overlapping region. This paper describes a systematical study on an accuracy enhancing interface treatment algorithm based on the back and forth error compensation and correction method (BFECC). By repetitively employing a low order interpolation technique (normally local 2\ts{nd} order) 3 times, this algorithm achieves local 3\ts{rd} order accuracy. Analytical derivations for 1D \& 2D cases are made, and the "super convergence" phenomenon (4\ts{th} order accuracy) is found for specific positioning of the donor and target grids. A set of numerical experiments based on various relative displacements, relative rotations, mesh ratios, and meshes with perturbation have been tested, and the results match the derivations. Different interface treatments are compared with 3D examples: corner flow and cavity flow. The component convergence rate analysis shows that the BFECC method positively affects the accuracy of solutions., Comment: 27 pages, 16 figures

The emergent two-dimensional (2D) ferromagnetic materials with unique magnetic properties have endowed great potential for next-generation spintronic devices with extraordinary merits of high flexibility, easy controllability, and high heretointegrability, which is expected to promote the development of Moore's Law continuously. However, it is extremely challenging to realize magnetic switching with ultra-low power consumption at room temperature. Here, we demonstrate the room-temperature spin-orbit torque (SOT) driven magnetization switching in a well-epitaxial all-van der Waals (vdW) heterostructure. The topological insulator Bi2Te3 not only helps to elevate the Curie temperature of Fe3GeTe2 (FGT) through interfacial exchange coupling but also works as a spin current source allowing to switch FGT at a low current density of 2.2 * 106 A cm2. A large SOT efficiency of 0.7 is measured at room temperature, and the thickness of FGT is further adjusted to reduce the influence of the thermal contribution on the second-harmonic signal. Furthermore, the temperature and thickness-dependent SOT efficiency prove that the large SOT in our system mainly originates from the nontrivial origin of topological materials. Our experiment has enabled an all-vdW SOT structure and lays a solid foundation for the implementation of room-temperature all-vdW spintronic devices in the future.

Recent research works for solving partial differential equations (PDEs) with deep neural networks (DNNs) have demonstrated that spatiotemporal function approximators defined by auto-differentiation are effective for approximating nonlinear problems, e.g. the Burger's equation, heat conduction equations, Allen-Cahn and other reaction-diffusion equations, and Navier-Stokes equation. Meanwhile, researchers apply automatic differentiation in physics-informed neural network (PINN) to solve nonlinear hyperbolic systems based on conservation laws with highly discontinuous transition, such as Riemann problem, by inverse problem formulation in data-driven approach. However, it remains a challenge for forward methods using DNNs without knowing part of the solution to resolve discontinuities in nonlinear conservation laws. In this study, we incorporate 1st order numerical schemes into DNNs to set up the loss functional approximator instead of auto-differentiation from traditional deep learning framework, e.g. TensorFlow package, which improves the effectiveness of capturing discontinuities in Riemann problems. In particular, the 2-Coarse-Grid neural network (2CGNN) and 2-Diffusion-Coefficient neural network (2DCNN) are introduced in this work. We use 2 solutions of a conservation law from a converging sequence, computed from a low-cost numerical scheme, and in a domain of dependence of a space-time grid point as the input for a neural network to predict its high-fidelity solution at the grid point. Despite smeared input solutions, they output sharp approximations to solutions containing shocks and contacts and are efficient to use once trained.

A new finite difference method on irregular, locally perturbed rectangular grids has been developed for solving electromagnetic waves around curved perfect electric conductors (PEC). This method incorporates the back and forth error compensation and correction method (BFECC) and level set method to achieve convenience and higher order of accuracy at complicated PEC boundaries. A PDE-based local second order ghost cell extension technique is developed based on the level set framework in order to compute the boundary value to first order accuracy (cumulatively), and then BFECC is applied to further improve the accuracy while increasing the CFL number. Numerical experiments are conducted to validate the properties of the method.

Although much significant progress has been made in the research field of object detection with deep learning, there still exists a challenging task for the objects with small size, which is notably pronounced in UAV-captured images. Addressing these issues, it is a critical need to explore the feature extraction methods that can extract more sufficient feature information of small objects. In this paper, we propose a novel method called Dense Multiscale Feature Fusion Pyramid Networks(DMFFPN), which is aimed at obtaining rich features as much as possible, improving the information propagation and reuse. Specifically, the dense connection is designed to fully utilize the representation from the different convolutional layers. Furthermore, cascade architecture is applied in the second stage to enhance the localization capability. Experiments on the drone-based datasets named VisDrone-DET suggest a competitive performance of our method., Comment: 10 pages, 5 figures

We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential terms in a prescribed dictionary. Noisy data make such identification particularly challenging. Our objective is to develop methods which are robust against a high level of noise, and to approximate the underlying noise-free dynamics well. We first introduce a Successively Denoised Differentiation (SDD) scheme to stabilize the amplified noise in numerical differentiation. SDD effectively denoises the given data and the corresponding derivatives. Secondly, we present two algorithms for PDE identification: Subspace pursuit Time evolution error (ST) and Subspace pursuit Cross-validation (SC). Our general strategy is to first find a candidate set using the Subspace Pursuit (SP) greedy algorithm, then choose the best one via time evolution or cross validation. ST uses multi-shooting numerical time evolution and selects the PDE which yields the least evolution error. SC evaluates the cross-validation error in the least squares fitting and picks the PDE that gives the smallest validation error. We present a unified notion of PDE identification error to compare the objectives of related approaches. We present various numerical experiments to validate our methods. Both methods are efficient and robust to noise.

Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying coefficients add complexity to the problem. We assume that the governing partial differential equation (PDE) is a linear combination of a subset of a prescribed dictionary containing different differential terms, and the objective of this paper is to find the correct coefficients. We propose a new direction based on the fundamental idea of convergence analysis of numerical PDE schemes. We utilize Lasso for efficiency, and a performance guarantee is established based on an incoherence property. The main contribution is to validate and correct the results by Time Evolution Error (TEE). The new algorithm, called Identifying Differential Equations with Numerical Time evolution (IDENT), is explored for data with non-periodic boundary conditions, noisy data and PDEs with varying coefficients. From the recovery analysis of Lasso, we propose a new definition of Noise-to-Signal ratio, which better represents the level of noise in the case of PDE identification. We systematically analyze the effects of data generations and downsampling, and propose an order preserving denoising method called Least-Squares Moving Average (LSMA), to preprocess the given data. For the identification of PDEs with varying coefficients, we propose to add Base Element Expansion (BEE) to aide the computation. Various numerical experiments from basic tests to noisy data, downsampling effects and varying coefficients are presented.