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In this paper, we develop the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for convection-diffusion equations with inhomogeneous Dirichlet, Neumann and Robin boundary conditions, along with high-contrast coefficients. For time independent problems, boundary correctors $\mathcal{D}^m$ and $\mathcal{N}^{m}$ for Dirichlet, Neumann, and Robin conditions are designed. For time dependent problems, a scheme to update the boundary correctors is formulated. Error analysis in both cases is given to show the first-order convergence in energy norm with respect to the coarse mesh size $H$ and second-order convergence in $L^2-$norm, as verified by numerical examples, with which different finite difference schemes are compared for temporal discretization. Nonlinear problems are also demonstrated in combination with Strang splitting., Comment: 36 pages.11 figures. Submitted to Journal of Computational Mathematics

Large Language Models (LLMs) are undergoing a period of rapid updates and changes, with state-of-the-art (SOTA) model frequently being replaced. When applying LLMs to a specific scientific field, it's challenging to acquire unique domain knowledge while keeping the model itself advanced. To address this challenge, a sophisticated large language model system named as Xiwu has been developed, allowing you switch between the most advanced foundation models and quickly teach the model domain knowledge. In this work, we will report on the best practices for applying LLMs in the field of high-energy physics (HEP), including: a seed fission technology is proposed and some data collection and cleaning tools are developed to quickly obtain domain AI-Ready dataset; a just-in-time learning system is implemented based on the vector store technology; an on-the-fly fine-tuning system has been developed to facilitate rapid training under a specified foundation model. The results show that Xiwu can smoothly switch between foundation models such as LLaMA, Vicuna, ChatGLM and Grok-1. The trained Xiwu model is significantly outperformed the benchmark model on the HEP knowledge question-and-answering and code generation. This strategy significantly enhances the potential for growth of our model's performance, with the hope of surpassing GPT-4 as it evolves with the development of open-source models. This work provides a customized LLM for the field of HEP, while also offering references for applying LLM to other fields, the corresponding codes are available on Github., Comment: 15 pages, 8 figures

In this paper, we combine the multiscale flnite element method to propose an algorithm for solving the non-stationary Stokes-Darcy model, where the permeability coefflcient in the Darcy region exhibits multiscale characteristics. Our algorithm involves two steps: first, conducting the parallel computation of multiscale basis functions in the Darcy region. Second, based on these multiscale basis functions, we employ an implicitexplicit scheme to solve the Stokes-Darcy equations. One signiflcant feature of the algorithm is that it solves problems on relatively coarse grids, thus signiflcantly reducing computational costs. Moreover, under the same coarse grid size, it exhibits higher accuracy compared to standard flnite element method. Under the assumption that the permeability coefflcient is periodic and independent of time, this paper demonstrates the stability and convergence of the algorithm. Finally, the rationality and effectiveness of the algorithm are verifled through three numerical experiments, with experimental results consistent with theoretical analysis.

This paper explores the application of the multiscale finite element method (MsFEM) to address steady-state Stokes-Darcy problems with BJS interface conditions in highly heterogeneous porous media. We assume the existence of multiscale features in the Darcy region and propose an algorithm for the multiscale Stokes-Darcy model. During the offline phase, we employ MsFEM to construct permeability-dependent offline bases for efficient coarse-grid simulation, with this process conducted in parallel to enhance its efficiency. In the online phase, we use the Robin-Robin algorithm to derive the model's solution. Subsequently, we conduct error analysis based on $L^2$ and $H^1$ norms, assuming certain periodic coefficients in the Darcy region. To validate our approach, we present extensive numerical tests on highly heterogeneous media, illustrating the results of the error analysis.

In recent years, medical information technology has made it possible for electronic health record (EHR) to store fairly complete clinical data. This has brought health care into the era of "big data". However, medical data are often sparse and strongly correlated, which means that medical problems cannot be solved effectively. With the rapid development of deep learning in recent years, it has provided opportunities for the use of big data in healthcare. In this paper, we propose a temporal-saptial correlation attention network (TSCAN) to handle some clinical characteristic prediction problems, such as predicting death, predicting length of stay, detecting physiologic decline, and classifying phenotypes. Based on the design of the attention mechanism model, our approach can effectively remove irrelevant items in clinical data and irrelevant nodes in time according to different tasks, so as to obtain more accurate prediction results. Our method can also find key clinical indicators of important outcomes that can be used to improve treatment options. Our experiments use information from the Medical Information Mart for Intensive Care (MIMIC-IV) database, which is open to the public. Finally, we have achieved significant performance benefits of 2.0\% (metric) compared to other SOTA prediction methods. We achieved a staggering 90.7\% on mortality rate, 45.1\% on length of stay. The source code can be find: \url{https://github.com/yuyuheintju/TSCAN}.

The chest X-ray is often utilized for diagnosing common thoracic diseases. In recent years, many approaches have been proposed to handle the problem of automatic diagnosis based on chest X-rays. However, the scarcity of labeled data for related diseases still poses a huge challenge to an accurate diagnosis. In this paper, we focus on the thorax disease diagnostic problem and propose a novel deep reinforcement learning framework, which introduces prior knowledge to direct the learning of diagnostic agents and the model parameters can also be continuously updated as the data increases, like a person's learning process. Especially, 1) prior knowledge can be learned from the pre-trained model based on old data or other domains' similar data, which can effectively reduce the dependence on target domain data, and 2) the framework of reinforcement learning can make the diagnostic agent as exploratory as a human being and improve the accuracy of diagnosis through continuous exploration. The method can also effectively solve the model learning problem in the case of few-shot data and improve the generalization ability of the model. Finally, our approach's performance was demonstrated using the well-known NIH ChestX-ray 14 and CheXpert datasets, and we achieved competitive results. The source code can be found here: \url{https://github.com/NeaseZ/MARL}.

The chest X-ray (CXR) is one of the most common and easy-to-get medical tests used to diagnose common diseases of the chest. Recently, many deep learning-based methods have been proposed that are capable of effectively classifying CXRs. Even though these techniques have worked quite well, it is difficult to establish whether what these algorithms actually learn is the cause-and-effect link between diseases and their causes or just how to map labels to photos.In this paper, we propose a causal approach to address the CXR classification problem, which constructs a structural causal model (SCM) and uses the backdoor adjustment to select effective visual information for CXR classification. Specially, we design different probability optimization functions to eliminate the influence of confounders on the learning of real causality. Experimental results demonstrate that our proposed method outperforms the open-source NIH ChestX-ray14 in terms of classification performance.

This paper presents and analyses a Constraint Energy Minimization Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving single-phase non-linear compressible flows in highly heterogeneous media. The construction of CEM-GMsFEM hinges on two crucial steps: First, the auxiliary space is constructed by solving local spectral problems, where the basis functions corresponding to small eigenvalues are captured. Then the basis functions are obtained by solving local energy minimization problems over the oversampling domains using the auxiliary space. The basis functions have exponential decay outside the corresponding local oversampling regions. The convergence of the proposed method is provided, and we show that this convergence only depends on the coarse grid size and is independent of the heterogeneities. An online enrichment guided by \emph{a posteriori} error estimator is developed to enhance computational efficiency. Several numerical experiments on a three-dimensional case to confirm the theoretical findings are presented, illustrating the performance of the method and giving efficient and accurate numerical.

Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this letter, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided modes. Our findings offer new opportunities for manipulating nonlinear optical fields with PT symmetry, which could further boost more exploration on on-chip nonlinear devices assisted by non-Hermitian optics., Comment: to be published in Frontiers of Physics

In this paper we present and analyze a constraint energy minimizing generalized multiscale finite element method for convection diffusion equation. To define the multiscale basis functions, we first build an auxiliary multiscale space by solving local spectral problems motivated by analysis. Then constraint energy minimization performed in oversampling domains is exploited to construct the multiscale space. The resulting multiscale basis functions have a good decay property even for high contrast diffusion and convection coefficients. Furthermore, if the number of oversampling layer is chosen properly, we can prove that the convergence rate is proportional to the coarse mesh size. Our analysis also indicates that the size of the oversampling domain weakly depends on the contrast of the heterogeneous coefficients. Several numerical experiments are presented illustrating the performances of our method., Comment: arXiv admin note: text overlap with arXiv:1704.03193

In this paper, we study the generalized multiscale finite element method (GMsFEM) for single phase compressible flow in highly heterogeneous porous media. We follow the major steps of the GMsFEM to construct permeability dependent offline basis for fast coarse-grid simulation. The offline coarse space is efficiently constructed only once based on the initial permeability field with parallel computing. A rigorous convergence analysis is performed for two types of snapshot spaces. The analysis indicates that the convergence rates of the proposed multiscale method depend on the coarse meshsize and the eigenvalue decay of the local spectral problem. To further increase the accuracy of multiscale method, residual driven online multiscale basis is added to the offline space. The construction of online multiscale basis is based on a carefully design error indicator motivated by the analysis. We find that online basis is particularly important for the singular source. Rich numerical tests on typical 3D highly heterogeneous medias are presented to demonstrate the impressive computational advantages of the proposed multiscale method.

In this paper, a strongly mass conservative and stabilizer free scheme is designed and analyzed for the coupled Brinkman-Darcy flow and transport. The flow equations are discretized by using a strongly mass conservative scheme in mixed formulation with a suitable incorporation of the interface conditions. In particular, the interface conditions can be incorporated into the discrete formulation naturally without introducing additional variables. Moreover, the proposed scheme behaves uniformly robust for various values of viscosity. A novel upwinding staggered DG scheme in mixed form is exploited to solve the transport equation, where the boundary correction terms are added to improve the stability. A rigorous convergence analysis is carried out for the approximation of the flow equations. The velocity error is shown to be independent of the pressure and thus confirms the pressure-robustness. Stability and a priori error estimates are also obtained for the approximation of the transport equation; moreover, we are able to achieve a sharp stability and convergence error estimates thanks to the strong mass conservation preserved by our scheme. In particular, the stability estimate depends only on the true velocity on the inflow boundary rather than on the approximated velocity. Several numerical experiments are presented to verify the theoretical findings and demonstrate the performances of the method.

In this paper, we first propose and analyze a novel mixed-type DG method for the coupled Stokes-Darcy problem on simplicial meshes. The proposed formulation is locally conservative. A mixed-type DG method in conjunction with the stress-velocity formulation is employed for the Stokes equations, where the symmetry of stress is strongly imposed. The staggered DG method is exploited to discretize the Darcy equations. As such, the discrete formulation can be easily adapted to account for the Beavers-Joseph-Saffman interface conditions without introducing additional variables. Importantly, the continuity of normal velocity is satisfied exactly at the discrete level. A rigorous convergence analysis is performed for all the variables. Then we devise and analyze a domain decomposition method via the use of Robin-type interface boundary conditions, which allows us to solve the Stokes subproblem and the Darcy subproblem sequentially with low computational costs. The convergence of the proposed iterative method is analyzed rigorously. In particular, the proposed iterative method also works for very small viscosity coefficient. Finally, several numerical experiments are carried out to demonstrate the capabilities and accuracy of the novel mixed-type scheme, and the convergence of the domain decomposition method., Comment: 25 pages, 7 figures