召集人：陈掌星（University   of Calgary）、林延平（Hong Kong Polytechnic University）、李剑（陕西科技大学）

时间：2024.12.15—2024.12.21

一   会议日程

二   会议摘要与专家简介

（按姓氏字母排序）

报告人 陈黄鑫（厦门大学）

报告题目

Efficient and physics-preserving algorithms for thermodynamically consistent flow models in porous media

报告摘要

Modeling and simulation of two-phase flow and gas flow in porous media are of great interest in the fields of hydrology and petroleum reservoir engineering. In this talk we will introduce a thermodynamically consistent mathematical model for incompressible and immiscible two-phase flow in porous media with rock compressibility. An energy stable numerical method will be introduced, which can preserve multiple physical properties, including the energy dissipation law, full conservation law for both fluids and pore volumes, and bounds of porosity and saturations. Then, a thermodynamically consistent model for multicomponent flow in porous media with rock compressibility and its energy-stable and conservative algorithms will be discussed. Furthermore, we will also introduce a thermodynamically consistent numerical method for gas flow in poroelasticity media, which is coupled with the single-phase compressible flow and poromechanics.

报告人简介

陈黄鑫，厦门大学数学科学学院教授。2006年获得湖南大学理学学士学位，2011年获中国科学院数学与系统科学研究院理学博士学位。主要从事自适应有限元方法、多重网格方法、间断有限元方法、多孔介质中的流动输运问题和拓扑优化问题的求解。成果发表在 Math. Comp., SINUM,  Numer. Math. 等计算数学领域著名期刊，主持国家自然科学基金优秀青年科学基金项目和面上项目等。

报告人 陈金如（南京师范大学）

报告题目

A nonconforming extended virtual element method for Stokes interface Problems

报告摘要

In this talk, we propose a nonconforming extended virtual element method, which combines the extended finite element method with the nonconforming virtual element method, for solving Stokes interface problems with the unfitted-interface mesh. By introducing some stabilization terms and penalty terms, as well as some special terms defined on non-cut edges of interface elements in the discrete bilinear form, we prove the discrete inf-sup condition and obtain optimal error estimates. It is shown that all results are not only independent of the mesh size and the viscosity coefficient, but also the interface position. Numerical experiments are performed to verify theoretical results.

报告人简介

陈金如，毕业于南京师范大学数学系，分别于 1986年7月、1989 年 7 月获得理学学士学位、理学硕士学位。硕士研究生毕业后留校任教。1998 年 7 月在复旦大学数学所获得博士学位。1998 年8 月至 2000 年 7 月在中科院计算数学所从事博士后研究工作。主要从事有限元方法，区域分解方法，多重网格方法，和界面问题的数值方法研究。先后应邀到香港、美国、日本、俄罗斯、德国、挪威等地区和国家参加国际学术会议。发表学术论文 80 多篇，主持完成 5 项国家自然科学基金项目，以骨干成员参加完成 2 项“973”项目，参加完成国家自然科学基金重点项目 2 项，目前主持1 项国家自然科学基金项目。研究成果获江苏省科技进步奖二等奖 1 项（排名第三），江苏省科学技术奖二等奖 1 项（排名第五）。曾任江苏省数学会副理事长。目前任江苏省数学会监事，江苏省数学会数学教育专业委员会主任，南京数学学会理事长，南京师范大学“大规模复杂系统数值模拟教育部重点实验室”副主任。

报告人 陈掌星（宁波东方理工大学、卡尔加里大学）

报告题目

数据与知识双驱动的油气智能大模型: 盖亚大模型

报告摘要

工业软件是整个中国工业体系中最为薄弱的环节，我国工业软件研发和应用远落后西方发达国家，80%以上关键技术软件依赖于国外进口，是当前最为卡住我们脖子的关键技术。尤其新一轮以GPT和SORA为代表的生成式人工智能大模型，正引领数字化转型、智能化发展的潮流。人工智能时代带来的伟大变革是深刻且广泛的，从底层技术革新到社会结构的重塑，从经济形态的转变到人们日常生活的细微之处，几乎无处不在。谁能赢得人工智能技术，谁就能引领未来科技创新。但工业软件, 尤其智能大模型的研发和应用，面临算力、存储及可解释性的极大挑战。本报告将介绍工业软件、数据驱动机器学习、融合物理和数据驱动机器学习以及未来地学领域人工智能大模型技术现状、面临的挑战与发展前景，重点介绍本研究团队研发的平行油藏数值模拟技术和油气领域知识与数据双驱动智能大模型: 盖亚大模型。

报告人简介

陈掌星，美国国家工程院院士，中国工程院外籍院士，加拿大皇家科学院院士、工程院院士，欧盟科学院院士，数学家、石油和天然气工程专家，宁波东方理工大学（暂名）创校讲席教授，加拿大卡尔加里大学国家讲席教授，中国石油大学（北京）教育部非常规油气国际合作联合实验室主任。主要从事人工智能技术与能源开发基础理论研究及工业应用。根据爱思维尔统计结果，在石油工程领域近 15 年内（2008-2023），其学术论文综合指标（包括论文数、他人引用数和H指数）全球排名第一。在包括《美国国家科学院院刊》等在内的期刊发表论文 1,200 篇，出版著作 24 部，在包括“世界顶尖科学家论坛”等在内的国际会议上作特邀学术报告 500 次，拥有 53 项发明专利，是 18 种国际杂志编委。曾获中国政府友谊奖、美国福特总统奖、加拿大最高科技奖、工业与应用数学菲尔兹奖、世界石油学会最高成就奖等。   

报告人 戴书洋（武汉大学）

报告题目

Phase field modeling of Shear-induced Amorphization in Alloy

报告摘要

Amorphization due to severe plastic deformation has been discovered in various crystalline materials. Despite its importance, developing a rigorous and general theory of strain-induced amorphization remains a significant challenge due to the intricate nature of modeling microstructural changes and deformation mechanisms. In this study, we propose a novel model integrated with elastic-plastic theory to shed light on shear-induced amorphization in nanocrystalline alloys. Our simulations suggest that amorphous nucleation is more likely to occur in high-stress regions, such as shear bands, and that the critical plastic strain for amorphization increases as grain size grows. These observations align with experimental data, indicating that our phase-field model captures the physical picture of shear-induced amorphization and can predict the threshold for amorphization.

报告人简介

戴书洋，武汉大学数学与统计学院教授。2017 年入选国家高层次青年人才项目。现任武汉工业与应用数学学会副理事长。研究方向为多尺度问题的建模、高效算法与优化，关注数学与材料科学以及医学等交叉领域中的计算优化问题等，在固体材料的多尺度建模与缺陷模拟计算、复杂异质体系高效算法、精准放疗优化算法等方面做出突出工作。主持多项国家自然科学基金、湖北省自然科学基金、湖北省重点实验室开放基金等，参与科技部重点研发、湖北省创新群体、湖北省科技重大项目等重大科研项目。

报告人 邓伟华（兰州大学）

报告题目

Multiscale Modelling and Simulation for Anomalous and Nonergodic Dynamics: From Statistics to Mathematics

报告摘要

 In recent decades, anomalous and nonergodic dynamics are topical issues in almost all disciplines. In 2004, the phrase "anomalous is normal" was used in a title of a PRL paper, which reveals that the diffusion of classical particles on a solid surface has rich anomalous behavior controlled by the friction coefficient, meaning that anomalous dynamics phenomena are ubiquitous in the natural world. This talk first introduces the dynamics from a physical and atomistic way, by considering the random walk of the diffusing particles, then derives the partial differential equations with integral-differential operators governing the PDFs of the various statistical observables. Finally, we discuss the (traditional and deep learning based) numerical methods for the newly build PDEs.

报告人简介

邓伟华，兰州大学数学与统计学院、兰州大学天然产物化学全国重点实验室，教授。研究方向为科学计算与数值分析、统计物理学和随机模拟、非线性动力学和反常扩散、非局部偏微分方程与随机表示，多尺度非遍历动力学模型、科学计算、深度学习算法。建立了粒子轨迹泛函分布的模型，针对模型给出了有效的计算方法，给出了具体的物理应用并做了大量的统计分析。在 Mathematics of  Computation、SIAM Journal on Numerical Analysis、Physical Review E 等刊物发表 SCI 论文共 60 余篇，被 SCI 他引 1400 多次。

报告人 段火元 (武汉大学)

报告题目

Wrong and correct convergent finite element methods for the Stokes equations with pressure Dirichlet boundary conditions   

报告摘要

 With local pressure-residual stabilizations as an augmentation to the classical Galerkin/least-squares (GLS) stabilized method, a new locally evaluated residual-based stabilized finite element method is proposed for a type of Stokes equations from incompressible flows. We focus on the study of a type of nonstandard boundary conditions involving mixed tangential velocity and  pressure Dirichlet boundary conditions; while the proposed method can be extended to deal with other nonstandard boundary conditions such as the mixed tangential Dirichlet and normal Neumann boundary conditions of velocity and the Navier-slip boundary conditions where no pressure boundary conditions are present. Typically, such equations also arise as a model from electromagnetism. Unexpectedly, in sharp contrast to the standard velocity Dirichlet boundary condition (i.e., the so-called no-slip boundary condition), neither the discrete Ladyženskaja-Babuška-Brezzi(LBB) inf-sup stable elements such as the well-known Mini element nor the stabilized methods such as the classical GaLS stabilized method could certainly ensure a convergent finite element solution for the nonstandard boundary conditions. It turns out that under nonstandard boundary conditions, the velocity solution could be very weak with its gradient not being square integrable; consequently, the discrete LBB condition or the Babuska weak coercivity may not be sufficient for the convergence.  The main purpose of this talk is to propose a new stabilized method for approximating the very weak velocity solution. For the new method with the key property of pressure-residual stabilizations, we can manage to prove the convergence with the error estimates for the very weak velocity solution. Numerical results are provided to illustrate the performance and the theoretical results of the proposed method. Theoretical and numerical results have shown that higher-order elements are generally necessary for very weak velocity solutions.

报告人简介

段火元，武汉大学数学与统计学院，教授，博士生导师。研究兴趣包括：偏微分方程数值解，有限元方法，科学计算，等等。

报告人 郭士民（西安交通大学）

报告题目

 IMEX spectral method for three-dimensional MHD-type system 

报告摘要

In this talk, we shall first constructing an efficient numerical scheme for three-dimensional Hall-MHD system. The Legendre-Galerkin spectral method is applied for spatial approximation. By introducing an artificial auxiliary variable, we employ Crank-Nicolson scheme for the temporal discretization with the explicit treatment of nonlinear terms. Then, we establish an efficient finite difference/Legendre-Galerkin spectral method for three-dimensional incompressible heat-conducting MHD system to simultaneously preserve several intrinsic multiphysics structures, namely, the mass conservation, the density conservation in L^2-norm, the kinetic-energy dissipation, and the heat-energy conservation.

报告人简介

郭士民，西安交通大学教授、博士生导师，主要研究方向为计算等离子体物理、高精度数值算法。在 SIAM Journal on Scientific Computing, Journal of Computational Physics 等期刊发表多篇学术论文，ESI 高被引论文 2 篇；主持国家自然科学基金面上项目、国家重点研发计划子课题等多项科研项目。博士学位论文入选“2016 年度陕西省优秀博士学位论文”，获 2019 年度陕西省自然科学奖二等奖。

报告人 何银年（西安交通大学，新疆大学）

报告题目

定常 Navier-Stokes 方程组差分有限元方法

报告摘要

In this work, a difference finite element method for the 3D steady Navier-Stokes equations ispresented. This new method consists of transmiting the finite element solution of the 3D steady NavierStokes equations into a series of the finite element solution of the 2D steady Oseen iterative equationswhich are solved by using the finite element pair satisfying the discrete inf-sup condition in a 2D domain ω.

In addition, we provide the existence and uniqueness of the difference finite element solutions of the3D steady Oseen iterative equations and deduce the optimal error estimates of the difference finiteelement solutions to the exact solution (u, p) of the 3D steady Navier-Stokes equations. finally, somenumerical tests are presented to show the accuracy and effectiveness of the proposed method.

报告人简介

何银年，西安交通大学数学与统计学院二级教授，博士生导师，国务院政府特殊津贴专家，新疆大学“天池学者”特聘教授，西安交通大学动力工程多相流国家重点实验室研究人员。曾担任陕西省计算数学学会理事长，陕西省数学学会常务理事，全国计算数学学会常务理事等。长期从事有关于Cahn-Hillard 方程，N-S 方程组，MHD 方程组及海洋流体动力学方程组的有限元及差分有限元方法的理论和算法研究，取得过许多重要理论分析结果。连续主持国家自然科学基金 8 项，部分研究成果获得 2007 年“国家自然科学二等奖”（第五完成人），2011 年“教育部自然科学二等奖”

（独立完成）并于 2016 年“陕西省科学技术一等奖”(第一完成人)。在国内外杂志发表 SCI 文章278 篇，其中 H 因子到 37，被 SCI 文章他引 4819 次，2014 - 2022 连续 9 年入选“爱思维尔中国高被引学者数学领域榜单”，在数学以及力学类国际顶尖杂志 SIAM J. Numer. Anal.、SIAM J. Sci Comp.、Numer. Math.、Math. Comp.、J. Differential Equations、J. Comp. Phys.、Comput. Methods Appl. Mech. Engrg.、IMA J. Numer. Analysis、Int. J. Numer. Methods Engrg. 等期刊发表文章37篇。

报告人 胡嘉顺（香港理工大学）

报告题目

A stabilized Arbitrary Lagrangian-Eulerian sliding interface method for fluid structure interaction with a rotating rigid structure

报告摘要

For fluid structure interaction with a rotating rigid structure, we introduced a novel sliding interface formulation, which improves existing methodologies with a skew-symmetric Nitsche’s stabilization term applied on an artificial sliding interface, alongside a rotational arbitrary Lagrangian-Eulerian framework. Our methodology includes a first-order full discretization that maintains energy-dissipating properties at the discrete level, ensuring numerical stability and accuracy. While prior contributions such as the original sliding interface method introduced by Bazilevs & Hughes (Comput. Mech., 43(1):143–150, 2008) have been significant, theoretical analyses such as the inf-sup condition on non-matching meshes have gone largely unaddressed. We fill this gap by proving the inf-sup condition within the context of the isoparametric finite element method, where meshes are not only non-matching but also overlapping, thus extending the applicability and robustness of our approach. Leveraging this inf-sup condition along with the inherent energy-dissipating properties, we establish the unique solvability of the fully discrete scheme. Through extensive numerical experiments, we illustrate the convergence, efficiency, and energy-dissipating property of the proposed method.

报告人简介

胡嘉顺，香港理工大学研究员。2021 年在清华大学数学科学系获得博士学位。研究兴趣包括流固相互作用的数值方法、曲率流下的表面演化和非线性薛定谔方程。

报告人 黄学海（上海财经大学）

报告题目

Distributional Finite Element curl div Complexes and Application to Quad Curl Problem and Stokes Equation

报告摘要

This talk addresses the challenge of constructing conforming finite element spaces for high-order differential operators in high dimensions, with a focus on the curl div operator in three dimensions. Tangential-normal continuity is introduced in order to develop distributional finite element curl div complexes. The spaces constructed are applied to discretize a quad curl problem and the Stokes equation, demonstrating optimal order of convergence. Furthermore, a hybridization technique is proposed, demonstrating its equivalence to nonconforming finite elements and weak Galerkin methods.

报告人简介

黄学海，上海财经大学讲席教授、博士研究生导师，研究方向为有限元方法。学术论文方面，在 Math. Comp.、SIAM J. Numer. Anal.、Numer. Math.、J. Sci. Comput. 等国际期刊发表 SCI 论文四十多篇。科研课题方面，正主持一项国家自然科学基金面上项目，主持完成国家自然科学基金面上项目、青年项目、数学天元项目、上海市自然科学基金原创探索项目和温州市科技计划项目各一项、浙江省自然科学基金项目两项。获中国计算数学学会优秀青年论文竞赛优秀奖，博士学位论文被评为上海市研究生优秀成果(学位论文)。

报告人 李剑（陕西科技大学）

报告题目

能源数学模型的高效数值方法研究及应用

报告摘要

主要研究一类简单的能源数学模型的高维、高阶、并行解耦数值方法，根据传统数值模拟结合实际给出数值模拟。

报告人简介

李剑，陕西科技大学数学与数据科学学院院长、教授二级、博士生导师。兼任中国工业与应用数学学会人工智能专业委员会委员，中国计算数学学会理事，陕西省统计学会副理事长等。5种国际期刊编委/副主编，美国《数学评论》评论员。先后获批享受国务院政府特殊津贴、教育部新世纪优秀人才、全国优秀教师、中组部/教育部/科技部/中科院“西部之光”访问学者、享受陕西省三秦人才津贴专家、陕西省“特支计划”区域人才、陕西省高教工委优秀党员、陕西青年科技新星、陕西青年科技奖和宝鸡突出贡献青年拔尖人才。主要从事偏微分方程高效数值方法研究、新能源问题可计算建模和流体计算人工智能方法研究。在国际计算数学或力学顶尖期刊 Numer. Math., SIAM J. Numer. Anal. 等发表SCI论文多篇，在 Springer 出版社、科学出版社出版中英文专著/教材共 3 部。与加拿大 AICISE 中心合作稠油开采报告 3 篇。作为项目负责人先后完成了教育部新世纪优秀人才支持计划项目、国家自然科学基金、教育部留学回国基金、陕西省特支计划项目、陕西青年科技新星等项目多项；科研成果获陕西省自然科学奖一等奖和陕西省自然科学奖二等奖各 1 项。

报告人 李继春（内华达大学拉斯维加斯分校）

报告题目

Analysis and simulation of a finite element method for a modified Cahn-Hilliard-Hele-Shaw system

报告摘要

In this talk, I'll talk about a nnew finite element method for solving a modified Cahn–Hilliard–Hele–Shaw system. The time discretization is based on the convex splitting of the energy functional in the modified Cahn–Hilliard quation, i.e., the high-order nonlinear term and the linear term in the chemical potential are treated explicitly and implicitly, respectively. Doing this leads to solving a linear system at each time step, which makes this method much more efficient. Unconditional energy stability and optimal error estimates are established for the proposed scheme.  Numerical results are presented to support our analysis.

报告人简介

Jichun Li is Professor of Mathematics and Director of Center for Applied Mathematics and Statistics at University of Nevada Las Vegas (UNLV). He got his BS from Nanjing University, and PhD from Florida State University. His previous positions include Postdoc Fellow at University of Texas at Austin, and Associate Director of Institute for Pure and  Applied Mathematics (IPAM) at University of California at Los Angeles (UCLA). Research areas include analysis of finite element methods, high-order compact difference methods, RBF meshless methods, and applications of PDEs in various areas. He has published over 160 SCI-indexed papers and 2 monographs (one in the famous Springer Series in Computational Mathematics, vol.43, Springer, 2013). Currently, he serves as Editor-in-Chief of "Results in Applied Mathematics", Managing Editor of "Computers & Mathematics with Applications" (both published by Elsevier).

报告人 李瑞（陕西师范大学）

报告题目

Modeling and numerical simulation for coupled free flow and dual porosity fractured porous media flow around a multistage fractured horizontal well in tight oil/gas reservoirs

报告摘要

In this talk, we propose and numerically solve a Stokes–dual–continuity–matrix–fracture model considering confined flow in dual porosity fractured porous media coupled with free flow in conduits. The flow in conduits is governed by the Stokes equation; the flow in dual porosity fractured porous media, which consists of both a dual porosity model and a reduced dual porosity fracture model, is described by a coupled dual-continuity–matrix–fracture model. The fluid interaction interface conditions between conduits, matrix, micro-fractures, and macro-fractures are constructed. The weak formulation is derived for the proposed model, and the well-posedness of the model is theoretically analyzed. We also propose a polyhedral discontinuous Galerkin finite element approximation for the Stokes flow in conduits and dual porosity model in the porous matrix, which is coupled with a conforming finite element scheme for the reduced dual porosity fracture model in the fracture. Optimal error estimates in a suitable energy norm are obtained. Two-dimensional numerical experiments are conducted to validate the proposed model and to demonstrate the features of both the model and the numerical method, such as the optimal convergence rate of the numerical solution; the detail flow characteristics around fractures, the matrix, and conduits; and the applicability to flow problems around multistage fractured horizontal wellbore.

报告人简介

李瑞，陕西师范大学数学与统计学院副教授。2017 年毕业于西安交通大学，获理学博士学位；主要从事多场耦合问题的可计算建模、数值方法程序设计与实现等方面的研究。在 J. Comput. Phys., J.Sci Comp. 等国内外期刊发表研究论文多篇。曾主持国家自然科学基金青年基金 1 项，陕西省自然科学基金面上项目、青年项目、高校科协青年人才托举项目各 1 项。

报告人 李晓丽（山东大学）

报告题目

Several linear and efficient methods for a coupled free flow-porous media system

报告摘要

In this talk, we shall first construct and analyze new first- and second-order implicit-explicit schemes for the unsteady Navier-Stokes-Darcy model to describe the coupled free flow-porous media system. The unconditional stability of both the first- and second-order IMEX schemes can be derived for the coupled system equipped with the Lions interface condition. We can also establish rigorous error estimates for the velocity and hydraulic head of the first-order scheme without any time step restriction. In addition, we also give first- and second-order implicit-explicit schemes for the closed-loop geothermal system, which includes the heat transfer between the porous media flow with Darcy equation in the geothermal reservoir and the free flow with Navier-Stokes equation in the pipe. Numerical examples are presented to validate the proposed schemes.

报告人简介

李晓丽，山东大学教授，博士生导师，国家高层次青年人才入选者，山东省杰青，山东大学杰出中青年学者。担任中国数学会计算数学分会常务理事。主要的研究领域为偏微分方程数值解与计算流体力学。在 SIAM J. Numer. Anal.、SIAM J. Sci. Comput.、Math. Comp.、J. Fluid Mech.、 Math. Mod. Meth. Appl. Sci. 及 J. Comput. Phys. 等计算数学高水平期刊发表学术论文多篇。入选 “博士后创新人才支持计划”，主持国家自然科学基金面上项目、重点项目子课题、青年项目等多个国家及省部级项目。

报告人 毛士鹏（中国科学院数学与系统科学研究院）

报告题目

A linear, mass-conserving, Gauss’s law preserving, charge-conserving, helicity-conserving finite element method for three dimensional MHD equations

报告摘要

We propose a novel structure-preserving finite element scheme for the three-dimensional magnetohydrodynamic (MHD) equations. The proposed scheme exactly preserves critical physical properties, including mass conservation, the magnetic Gauss\'s law, and charge conservation. Additionally, it conserves total energy and magnetic helicity in the inviscid and ideal MHD limits, as well as fluid helicity in the absence of magnetic fields. To the best of our knowledge, this is the first numerical method that simultaneously preserves all these properties. Another major advantage of our method over existing helicity-preserving schemes is its linearity and unconditional stability, which significantly reduces computational cost. For the resulting large linear systems, we develop efficient block preconditioners that remains robust at high fluid and magnetic Reynolds numbers by incorporating techniques such as the augmented Lagrangian method and mass augmentation. A series of numerical experiments demonstrate that our method is accurate, stable, and capable of preserving all the stated physical properties.

报告人简介

毛士鹏，中科院数学与系统科学研究院研究员、博士生导师，中科院大学岗位教授。2008 年博士毕业于中科院数学与系统科学研究院，2008 - 2012 先后在在法国国家信息自动化研究院（INRIA）以及在瑞士苏黎世高工 (ETH Zurich) 做博士后和研究助理。主要研究兴趣为有限元方法及其应用，多物理场耦合计算，计算流体力学和磁流体力学等。在 Math. Comp., Numer. Math.、SIAM 系列，M3AS 等杂志上发表论文 80 余篇，曾获中科院院长奖，中科院朱李月华优秀教师奖等，入选中科院青促会会员，主持和参加十余项基金委和科技部项目。

报告人 梅立泉（西安交通大学）

报告题目

星系演化的数值模拟及数据挖掘

报告摘要

宇宙中包括行星形成、太阳耀斑、恒星形成、太阳以及恒星星风、粒子加速、黑洞吸积与喷流、伽玛射线暴、黑洞撕裂恒星事件、超新星爆发、星系形成与演化、宇宙大尺度结构等现象都是由等离子体的原理和规律描述的。其中活动星系核反馈是星系中心超大质量黑洞在吸积过程中通过释放电磁辐射、风、喷流对宿主星系产生的反馈作用，这一过程对星系核球、星系及星系团中的气体分布与恒星形成都产生重要影响，是研究星系形成与演化的关键物理过程。本文主要介绍天体物理中黑洞吸积、活动星系核反馈过程，以及其中的数学问题，研究其数学模型求解的数值方法，对黑洞吸积和活动星系核反馈的数值模拟，以及对基于活动星系核反馈的星系演化结果的机器学习。

报告人简介

梅立泉，1997年获得计算数学专业博士学位，现在为西安交通大学数学与统计学院教授、博士生导师。陕西省工业与应用数学学会秘书长。主要研究方向为偏微分方程数值解、计算物理、数据挖掘。主持国家自然科学基金5项、973项目子课题3项，获欧洲专利、德国专利两项，获省部级自然科学奖2 项；已在 SIAM J. Sci. Comput., Comp. Meth. in Appl. Mech. Engi., J. Comput. P-hys., Appl. Math. Model., Appl. Math. Lett., Comput. Phys. Commun., Annals of Phys., Plasma Sources Sci. Tech., Plasma Phys. Cont. Fusion, Appl. Math. Comput., Phys. Plasmas, ApJ, MNRAS 等国际知名期刊上发表SCI论文150多篇，研究成果被他人多次引用。

报告人  石东洋（郑州大学，烟台大学）

报告题目

Superconvergence analysis of low-order mixed finite element method for time-dependent incompressible MHD equations

报告摘要

In this talk, we will present some new superconvergence error estimates of the backward Euler semi-implicit full discrete scheme for the time-dependent incompressible MHD equations with low-order mixed finite element method. Some innovative high-accuracy estimates of magnetic fields are introduced as the cornerstone for achieving superconvergence outcomes. By introducing a time-discrete auxiliary system, the unconditional boundedness of numerical solutions in -norm is obtained. And then without the limitation of mesh size h and time step , the superclose and superconvergence behavior is strictly derived using the interpolation post-processing technique. At the same time, some numerical results are provided to verify the theoretical findings.

报告人简介

石东洋，西安交通大学理学博士，东京工业大学博士后，河南省省级重点学科——计算数学学科带头人、学科特转教授、河南省学术与技术带头人，河南省优秀专家，河南省高层次人才，河南省创新人才培养工程专家，河南省数学首席科普专家，河南省优秀教师，河南省首批优秀研究生指导教师（2022）、中国科协和教育部中学生美才计划十周年（2013- 2022）优秀导师，河南省数字图形图像学会副理事长；中国科协《中学生英才计划》河南省数学学科组长；全国大学生数学建模竞赛河南省赛区专家组副组长。国家自然科学基金项目（青年、面上，重点、杰青）通讯评审专家，主持国家自然科学基金 7 项（其中面上项目 6 项），省部级项目 8 项，发表SCI论文 220 余篇，培养硕士、博土 130 余人，参编国家《数学大辞典》，获“中国百篇最具影响国内学术论立”  2 次。获省优秀科技成果及论文奖 20 项，2021 年获河南省人民政府科学技术奖——白然科学奖二等奖。

报告人 王波（河南大学）

报告题目

Fully discrete finite element numerical schemes for two kinds of active fluid models 

报告摘要

In this talk, we use fully discrete finite element numerical schemes to solve two kinds of active fluid models that describe the collective and organized motions of active fluid. The unique solvability, unconditional stability and error estimates of the numerical schemes are derived through rigorous theoretical analysis. Finally, numerical experiments are presented to verify the efficiency and accuracy of the proposed schemes.

报告人简介

王波，河南大学教师中心副主任，数学与统计学院教授，博士研究生导师，河南省高校青年骨干教师，河南大学教学名师，河南省教学标兵，河南省地球系统观测与模拟重点实验室副主任，中国工业与应用数学学会油水资源数值方法专业委员会委员。主要从事偏微分方程数值解法及其应用研究，主持或参与 6 项国家自然科学基金项目，6 项省部级项目；发表 40 余篇学术论文。河南省一流课程《高等数学》课程主持人，国家一流课程《数学分析》参与人，主持河南省重点教改项目 2 项，获河南省教学成果一等奖 1 项，二等奖 2 项，主编《高等数学》、《大学数学先修课》教材，长期从事《高等数学》、《数学分析》等专业基础课程的教学和研究工作。

报告人 王坤（重庆大学）

报告题目

Positivity-preserving finite element method for the chemotaxis(-fluid) equations 

报告摘要

In this talk, we consider some positivity-preserving finite element methods for solving the chemotaxis(-fluid) equations. In the first part, based on the flux-corrected transport technique，we develop a fully decoupled, linear, positivity-preserving and stable finite element scheme for solving the chemotaxis–fluid equations, in which we only need to solve several linearized sub-problems at each time step. The stability and error estimate of the scheme are proved. In the second part, based on the function transformation, we study a mass conservation and positivity-preserving finite element method for the chemotaxis equations. The stability and error estimate of the method are also proved. A series of numerical examples are shown to verify the theoretical predictions.

报告人简介

王坤，重庆大学数学与统计学院副教授、硕士生导师；主要从事偏微分方程数值解、科学计算等方向的研究，具体的包括复杂流体力学方程及其耦合问题、趋化模型和声波方程的数值分析与模拟等，其结果曾在 SIAM Journal of Numerical Analysis、Mathematics of Computation、Journal of Comp-utational Physics、Computer Methods in Applied Mechanics and Engineering 等杂志上发表。

报告人 吴朔男（北京大学）

报告题目

Stabilized Finite Element Methods and Fast Solvers for H(curl) Vector Field Convection-Diffusion Problems

报告摘要

Convection-diffusion equations, as one of the fundamental models for describing the coupling of multiple physical fields, find wide applications across various domains. Traditionally, the unknown functions in convection-diffusion equations are scalar functions. However, in recent years, the importance of convection-diffusion equations in problems involving vector fields such as electromagnetic fields has been increasingly recognized, leading to more complex mathematical formulations and structures of the convection terms. Building upon numerical methods for scalar convection-diffusion problems, this talk discusses two stabilized finite element discretization methods for H(curl) vector field convection-diffusion equations: upwind methods and exponential fitting methods. The former introduces stabilization terms by incorporating convection velocity information into the variational formulation, while the latter utilizes characteristics of boundary layer solutions to incorporate exponential functions into the scheme design. Furthermore, solvers for scalar convection-diffusion problems can be analogously adapted to construct solvers for H(curl) vector problems. We will analyze smoothers and multigrid algorithms from the perspective of Local Fourier Analysis (LFA). 

报告人简介

吴朔男，分别于 2009 年和 2014 年在北京大学数学科学学院获得学士和博士学位，2014 年至 2018年在美国宾州州立大学进行博士后研究，2018 年加入北京大学数学科学学院信息与计算科学系，现任副教授/研究员。主要研究方向为偏微分方程数值解，研究内容包括：磁流体力学中的磁对流的稳定离散、非线性、高阶椭圆型方程的非协调有限元的构造和分析，空间分数阶问题的离散和快速求解器等。研究工作发表在 Math. Comp., Numer. Math., SIAM J. Numer. Anal. 等核心期刊。

报告人 谢小平（四川大学）

报告题目

An energy-stable mixed finite:element method for Rosensweigferrofluid flow mode

报告摘要

We develop a mixed finite element method for the Rosensweig'sferrofluid flow model. First, we establish some regularity results folthe weak solution. Next, for the spatial semi-discretization of themodel using mixed finite elements we show that energy inequality ofthe continuous equation is preserved and give optimal error estimatesin $L^infty(L^2)$ and $L^2(H^1)$ norms. For the full discretizationusing implicit Euler scheme we show the existence and uniqueness of solutions, the unconditional stability and optimal error estimates.Finally, we provide numerical experiments to verify the theoreticalresults.

报告人简介

谢小平，四川大学数学学院教授(博导)，四川省学术和技术带头人，教育部新世纪优秀人才，德国洪堡学者。现兼任四川省普通本科高等学校数学类教学指导委员会秘书长，中国工业与应用数学学会油水资源数值方法专业委员会副主任委员。主要从事偏微分方程数值解相关领域研究工作。曾获教育部自然科学二等奖。

报告人 徐岩 (中国科学技术大学)

报告题目

High order energy stable adaptive method for phase transition problem

报告摘要

In this talk, we present high order energy stable adaptive method for phase transition problem. To bridge this gap we first write the pressure into a free energy function form and introduce the velocity as a variable, then we use an extra auxiliary variable containing both the free energy function and the square of the velocity. These auxiliary variables are chosen in the stability analysis as test functions for the density and momentum balance equations. To save computing time and to capture the thin interfaces more accurately, we extend the discretization with a mesh adaptation method. Given the current adapted mesh, a criterion for selecting candidate elements for refinement and coarsening is adopted based on the locally largest value of the density gradient. A strategy to refine and coarsen the candidate elements is then provided. Numerical experiments are provided to demonstrate the theoretical results, in particular on adaptive meshes.

报告人简介

徐岩，中国科学技术大学数学科学学院教授。2005 年于中国科学技术大学数学系获计算数学博士学位。2005 - 2007 年在荷兰 Twente 大学从事博士后研究工作。2009 年获得德国洪堡基金会的支持在德国 Freiburg 大学访问工作一年。主要研究领域为高精度数值计算方法。2008 年度获全国优秀博士学位论文奖，2017 年获国家自然科学基金委“优秀青年基金”, 2017 年获中国数学会计算数学分会第二届“青年创新奖”。徐岩教授入选了教育部新世纪优秀人才计划，主持国家自然科学基金面上项目、德国洪堡基金会研究组合作计划(Research Group Linkage Programme)、霍英东青年教师基础研究课题等科研项目。徐岩教授担任中国数学会计算数学分会理事，担任 SIAM  Journal on Scientific Computing, Journal of Scientific Computing、Advances in Applied Mathematics and Mechanics、Communication on Applied Mathematics and Computation、《计算物理》等杂志的编委。

报告人 徐振礼（上海交通大学）

报告题目

Fast Poisson Solvers for PNP and Vlasov-Poisson equations

报告摘要

We introduce fast Poisson solvers for structure-preserving numerical methods for models in plasma simulations including Poisson-Nernst-Planck (PNP) equations and Vlasov-Maxwell/Poisson equations. We first discuss an idea of designing numerical methods based on the Maxwell-Ampère Nernst-Planck equations which is equivalent to the PNP, where the curl-free relaxation is used to solve the electric field. We next construct curl-free basis functions for the Vlasov-Ampère equations which is equivalent to the Vlasov-Poisson equations. The scheme with energy conservation is designed, together with an asymptotic-preserving preconditioner such that the scheme can simulate systems at the quasi-neutral limit.  Numerical results are present to show the attractive performance of the new algorithms.

报告人简介

徐振礼，教授，分别于 2001、2003 和 2007 年从中国科学技术大学获得本科、硕士和博士学位。曾任美国北卡罗莱纳大学夏洛特分校博士后，德国斯图加特大学洪堡学者。2010 年加入上海交通大学任特别研究员，2016 年晋升正教授，2019 - 2021 年任数学科学学院副院长，2021 年起任教务处副处长。2010 年获得教育部新世纪优秀人才计划，2012 年入选中组部青年拔尖人才计划，2023年获国家自然基金杰出青年基金资助。担任 AAMM、CMS 和 MCA 等杂志编委。研究方向为快速算法和高性能计算、多体现象的建模和分析、分子动力学算法和偏微分方程的数值方法等等。

报告人 杨伟（湘潭大学）

报告题目

Time-domain mathematical modeling, finite element simulation, and design in complex anisotropic electromagnetic metamaterials

报告摘要

In this talk, we present a time-domain mathematical model, finite element methods, and related numerical theories for the electromagnetic propagation problem in three-dimensional anisotropic metamaterials. The model is capable of simultaneously characterizing the linear and nonlinear properties of materials. In terms of linear properties, we employ a designed finite element method to create five types of hyperbolic metamaterials within the 50-400nm wavelength range, and numerically verify their optical performance across a wide frequency spectrum. Additionally, by combining linear hyperbolic metamaterials with nonlinear materials, we simulate and design a nonlinear hyperbolic metamaterial, effectively enhancing the third harmonic generation of electromagnetic materials using hyperbolic materials.

报告人简介

杨伟，教授，博士生导师，现任湘潭大学教务处副处长。长期从事研究超材料中电磁波传播问题的建模与数值方法，在国际 SCI 期刊发表论文 40 余篇，其中包括计算数学领域权威期刊 SIAM J. Numer. Anal., SIAM J. Sci. Comput., SIAM J. Appl. Math. ,Math. Comput., J. Comput. Phys. 等，SCI 他引 400 余次。主持国家自然科学基金面上项目 2 项，青年项目 1 项，湖南省杰出青年基金项目 1项，作为核心成员参与国自科重大研究计划 2 项，国家重点研发计划项目 1 项，国防科工局国防基础项目 1 项、湖南省 JMRH 项目 1 项。2022 年入选湖南省“芙蓉学者奖励计划”青年学者、2016年获第三届中国工业与应用数学学会优秀青年学者奖。

报告人 尹小龙（宁波东方理工大学）

报告题目

数据哪里来？

孔隙尺度计算与复杂微流控可视化实验在数据时代渗流力学研究中的应用

报告摘要

传统的渗流力学研究较少涉及多孔介质内部的细致流动特征。首先，大多数多孔介质不透明，难以对其内部流动进行观察和测量；其次，多孔介质内部的孔隙结构与流动高度复杂，难以建立微观复杂流动结构与宏观渗流特征之间的关联。如何跨越尺度，寻找合适参数表征多孔介质内部的复杂孔隙结构与流动，构建简洁而优秀的渗流本构关系，是渗流力学研究中的一个困难且根本的问题。本报告将介绍孔隙尺度直接数值模拟和具有复杂结构的微流控渗流可视化实验，汇报课题组使用以上手段获得微观渗流数据、研究微观宏观关联过程中获得的一些结果与体会。以智能的方法寻找微观数据中存在的规律并将其与宏观特征进行关联，或将产生对渗流过程更深刻的认识。

报告人简介

尹小龙，宁波东方理工大学（暂名）工学部教授，国家级高层次人才计划获得者。从事渗流力学、多相流流体力学、流体相态方向上的理论与实验研究，回国前任教于美国科罗拉多矿业学院石油工程系并担任副系主任。目前担任国际石油工程师协会（SPE）油藏委员会委员、国际多孔介质学会（Interpore）中国分会委员、Advanced Powder Technology 杂志副编委。研究成果应用于油气开发、二氧化碳地质封存等能源资源地质工程项目。

报告人 翟起龙（吉林大学）

报告题目

Weak Galerkin finite element method for interface problems with curved interface

报告摘要

In this work, we develop a weak Galerkin finite element scheme for the Stokes interface problems with curved interfaces. The conventional numerical schemes rely on the use of straight segments to approximate the curved interfaces and the accuracy is limited by geometric errors. Hence in our method, we directly construct the weak Galerkin finite element space on the curved cells to avoid geometric errors. Theoretical analysis and a series of numerical experiments demonstrate that errors reach the optimal convergence orders under both the energy norm and the L2 norm.

报告人简介

翟起龙，吉林大学副教授，主要从事特征值问题高精度数值方法领域的研究，特别是对求解偏微分方程特征值问题的非标准有限元方法以及深度学习方法进行了深入探索，在计算数学高水平期刊发表SCI论文30余篇。翟起龙于2022年入选首届中国工业与应用数学学会青年人才托举工程项目，同年获吉林省自然科学奖一等奖（第二完成人），主持国家然科学基金面上项目、青年基金等项目。

报告人 张继伟（武汉大学）

报告题目

An efficient FEM framework for n-dimensional nonlocal problems

报告摘要

Nonlocality brings many challenges to the implementation of finite element methods (FEM) for nonlocal problems, such as large number of the query and invoke operations on the meshes. Furthermore, the interactions are usually limited to Euclidean balls, so direct numerical integrals often introduce numerical errors, so we have to carefully deal with interactions between the ball with finite elements, such as using ball-approximation strategies. Moreover, the parallel solution of nonlocal problems is more complex to implement than the parallel solution for local problems. Therefore, it is of great significance to propose efficient and general algorithms for solving nonlocal problems. In this talk, we present an efficient representation and construction method of approximate ball based on combinatorial maps and an efficient parallel algorithm for assembly of nonlocal linear systems. In order to conveniently and efficiently deal with numerical integrals over the intersection region of an element with the ball, a new ball-approximation method based on Monte Carlo integrals, the fullcaps method, is also proposed.

报告人简介

张继伟，男，武汉大学数学与统计学院教授，博士生导师。2009 年在香港浸会大学获得博士学位，随后在南洋理工大学和纽约大学克朗所从事博士后研究，2014 年前往北京计算科学研究中心工作，2018 年到武汉大学工作。主要研究领域包括偏微分方程和非局部模型的数值解法，以及神经科学的建模与计算，得到了国家自然科学基金重点、面上等项目的支持。在包括 SINUM，SISC，MCOM，JCNS 等国际知名期刊上发表学术论文90余篇。

报告人 秦毅（陕西科技大学）

报告题目

An Adaptive Time Filter Algorithm with Different SubdomainTime Steps for the 3D Unsteady-State Triple-Porosity Stokes Model

报告摘要

In this paper, an adaptive time filter algorithm with different subdomain variable time steps for the 3D unsteady-state triple-porosity Stokes model is proposed and analyzed. The main feature of this algorithm is the use of two different time steps in two different subdomains. Specifically, a larger step size is used in a porous medium region with a smaller flow velocity, and a smaller step size is used in a free-flow region. In addition, the central advantage of this algorithm is that it combines the advantages of a time filter algorithm and variable time steps in different subdomains, and constructs a corresponding adaptive algorithm to further improve computational efficiency. The stability and secondorder convergence of the algorithm are established, and its performance is validated through numerical experiments.

报告人简介

秦毅，副教授，硕士生导师。中国工业与应用数学学会青年托举人才，现任中国数学会计算数学分会理事，陕西省计算数学学会理事，美国数学评论评论员。受国家留学基金委资助赴美国匹兹堡大学 William Layton 教授处交流访问 1 年。已在 SIAM J. Numer. Anal. 等期刊发表学术论文 15 篇，主持国家自然科学基金青年项目 1 项、陕西省教育厅青年创新团队项目 1 项，获陕西省工业与应用数学学会青年优秀论文一等奖。

报告人 曹陆玲（陕西科技大学）

报告题目

A Local and Parallel FEMs for Super-Hydrophobic Proppants in a Hydraulic Fracturing System based on a 2D/3D Transient Triple-Porosity Navier-Stokes Model

报告摘要

A hydraulic fracturing system with super-hydrophobic proppants is characterized by a transient triple-porosity Navier-Stokes model. For this complex multiphysics system, particularly in the context of three-dimensional space, a local parallel and non-iterative finite element method based on two-grid discretizations is proposed. The underlying idea behind utilizing the local parallel approach is to combine a decoupled method, a two-grid method and a domain decomposition method. The strategy allows us to initially capture low-frequency data across the decoupled domain using a coarse grid. Then it tackles high-frequency components by solving residual equations within overlapping subdomains by employing finer grids and local parallel procedures at each time step. By utilizing this approach, a significant improvement in computational efficiency can be achieved. Furthermore, the convergence results of the approximate solutions from the algorithm are obtained. Finally, we perform 2D/3D numerical experiments to demonstrate the effectiveness and efficiency of the algorithm as well as to illustrate its advantages in application.

报告人简介

曹陆玲，副教授，硕士生导师。湘潭大学计算数学专业硕士，西安交通大学计算数学专业博士，曾赴加拿大卡尔加里大学石油化工系交流访学 1 年。现为陕西科技大学 2022 年高水平博士人才，中国优选法统筹法与经济数学研究会经济数学与管理数学分会第八届理事。已在 Journal of ScientificComputing 等国际知名 SCI 学术期刊上发表科研论文 6 篇，主持陕西省科技厅青年项目 1 项，陕西省博士后科研项目 1 项。

三   学生论坛

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报告人 陈乐乐（陕西科技大学）

报告题目

A third-order variable time step algorithm for the coupled multiphysics heat convection model

报告摘要

Heat convection plays a crucial role in optimizing energy extraction processes, influencing the efficiency and thermal dynamics of various systems. This paper develops, analyzes and tests a variable time step second order backward differentiation formula plus time filter (BDF2-TF) algorithm specifically for a three-dimensional closed-loop geothermal system model. By applying a three-step linear time filter method to the second-order backward differentiation formula, we eliminate low-order errors and achieve third-order accuracy in time while ensuring stability and hardly increasing the additional computational complexity. When the adjacent time step ratio τn ≈ τn−1 ∈ (0, 1.1119], we proved the stability and third order convergence for the variable time step BDF2-TF algorithm. The proposed algorithm’s effectiveness, stability, third-order convergence, and broad applicability are verified through three-dimensional exact solutions experiments and the simulation of geothermal energy extraction using a simplified coaxial pipeline.

报告人 陈晓勇（陕西科技大学）

报告题目

Modeling and numerical simulation for two-phase ferrofluid flows with different densities and viscosities

报告摘要

By using phase field techniques, a model describing the behavior of two-phase ferrofluid flows with different densities and dynamic viscosities is established. This model is a coupled nonlinear multiphysics

PDE system consisting of Cahn-Hilliard equations, Navier-Stokes equations, magnetization equation and magnetostatic equation. By reformulating the magnetic potential equation, applying the artificial compressibility method, utilizing the implicit-explicit scheme for treating the nonlinear terms, and adding several stabilization terms, we propose a linear, decoupled and fully discrete finite element method approximation for the established model. And it is strictly proved to be unconditionally stable. Several informative numerical experiments, including an accuracy test, deformation of a ferrofluid droplet, one or two air bubbles rising in ferrofluids, a controllable ferrofluid droplet in a Y-shape domain, and the Rosensweig instability under nonuniformly applied magnetic field, are performed to illustrate various features of the proposed model and scheme.

报告人 高卓语（陕西科技大学）

报告题目

A Local Parallel Fully Mixed Finite Element Method for Superposed Fluid and Porous Layers

报告摘要

Numerical simulation of the geothermal energy extraction process, described by the transient Navier–Stokes–Darcy–Boussinesq system of equations, is important for achieving the scientific collection and utilization of geothermal resources. Fluid velocity is a crucial parameter for improving geothermal energy recovery and ensuring efficient and stable operation of geothermal systems. The fully mixed form not only solves for the fluid velocity u and the pressure p simultaneously, but also captures fluid changes now as well as after they are predicted. In addition, geothermal systems in practical problems often have large spatial areas, which makes it necessary to use space efficient parallel algorithms. The key idea of the local parallel finite element based on two grid method is to first use a coarse grid globally to obtain low-frequency solutions decoupled across domains, and then at each time step, solve a series of local residual equations on overlapping subdomains with fine grids using a local parallel algorithm to obtain high-frequency solutions. This algorithm significantly improves computational efficiency. Finally, we validate the effectiveness and efficiency of this algorithm through numerical experiments.

报告人 李少轩（陕西科技大学）

报告题目

Neural Network-based Coupled Complex Fluid Model: Application of MC-CDNNs and Kolmogorov–Arnold Networks Methods

报告摘要

The study of neural networks for solving fundamental differential equations has been very well developed, while the study of neural networks is less involved in solving complex fluid coupling problems. Traditional physically-informed neural networks are more fixed in the constraint treatment of the equations, have not been well supported theoretically in the solution process, and deal with complex stochastic problems and high gradient problems, which is a major challenge in the research. In this report, we will extend the application of neural networks in coupled fluid problems based on the Monte Carlo method and MC-CDNN method of neural networks and parallel solution method of KANs, and verify their potential application in simulation through some numerical experiments.

报告人 刘坤昊（陕西科技大学）

报告题目

Inverse problem of data assimilation for shale oil model based on physics-informed neural networks

报告摘要

Proper analysis of velocity and pressure fields in shale oil models is critical for efficient shale oil recovery. In some situation, it is difficult to solve partial differential equations (PDEs) by conventional numerical algorithms without the completely model boundary information. This type of problem of prediction of velocity and pressure fields with unknown boundary information is an inverse problem of data assimilation. In this paper, we propose an inverse problem solving method based on physics-informed neural networks (PINNs) with respect to shale oil modelling. We use incomplete data to train neural networks and give an estimate of the L^2 error in the paradigmatic sense. It can be found that adding additional penalty parameter to the loss function can lead to better PINNs prediction in this inverse problem. Finally in the experiments, we validate the generalization ability of PINNs in solving the inverse problem of data assimilation by an example with a noise term.

报告人 孙洁琪（陕西科技大学）

报告题目

Few-shot classification with fork attention adapter

报告摘要

小样本学习是目前深度学习领域的研究热点和重要方向之一，在图像分类、图像分割等计算机视觉任务中具有广泛的应用。然而，在方法上依然存在许多问题值得深入探究，如基于单一低分辨表征对的相似度计算的有效性以及过度依赖小规模细粒度训练任务。针对以上两个问题，本次报告主要汇报的内容如下：1. 为了缓解单一表征相似度量的不稳定性，我们提出了叉状注意适配器(Fork Attention Adapter, FA-adapter)小样本图像分类方法。该方法可以无缝地与新生成的细微特征建立密集特征的相似性; 2. 结合迁移学习的思想，我们重新审视基于度量的元学习策略，提出了一种基于知识迁移(FA-Adapter++)的细粒度小样本图像分类方法。在该方法中，元训练阶段划分为元预训练阶段及元微调阶段。模型通过元预训练构建初始化作为先验知识，再利用先验知识推断细粒度表征交互和相关性，目的是提高模型在有限训练类别下的泛化能力。上述方法在经典小样本数据集mini-ImageNet, tiered-ImageNet, CUB-200-2011 以及 FGVC-Aircraft 等中进行 5-way 1-shot 及 5-way 5-shot 测试，分类精度得到了一致且显著的提高。