一周活动预告（10.17-10.23）
请查收。
目录：
A relaxed inertial and viscosity method for split feasibility problem and applications to image recovery（王宜举）
Neural Operator for Multidisciplinary Engineering Design（Zhengyu Huang）
Weak convergence analysis of an explicit time-steppping fully discrete scheme for SPDEs with polynomialnonlinearity（王小捷）
Superconvergence of discontinuous Galerkin methods（张智民）
再探增广拉格朗日法（丁超）
Two-sample testing of high-dimensional linear regression coefficients via complementary sketching（高凤楠）
Energy stable schemes for gradient flows based on the DVD method（黄记祖）
Multiscale Finite Element Methods for advection-diffusion problems (Professor Frederic Legoll)
Convergence analysis of RBF contour integral methods forhigh-dimensional option pricing PDEs（马敬堂）
1. A relaxed inertial and viscosity method for split feasibility problem and applications to image recovery
报告人: 王宜举 教授（曲阜师范大学）
报告时间: 2022-10.17 9:30-11:30
报告地点: 腾讯会议ID: 804-537-098 会议密码:221017
信息来源:
http://www2.scut.edu.cn/math/2022/1013/c10160a483837/page.htm
报告摘要:
In this talk, by combining Polyak's inertial extrapolation technique for minimization problem with the viscosity approximation for fixed point problem, we develop a new type of numerical solution method for split feasibility problem. Under suitable assumptions, we establish the global convergence of the designed method. The given experimental results applied on the sparse reconstruction problem show that the proposed algorithm is not only robust to different levels of sparsity and amplitude of signals and the noise pixels but also insensitive to the diverse values of scalar weight. Further, the proposed algorithm achieves better classification performance compared with some other algorithms for image recovery.
（灰色区域内上下滑动阅读全部内容）
2. Neural Operator for Multidisciplinary Engineering Design
Speaker: Zhengyu Huang（California Institute of Technology）
Time: 2022-10.18 10:00-11:00
Venue: Tencent Meeting ID: 532269265 Password: 969411
Info Source:
https://ins.sjtu.edu.cn/seminars/2177
Abstract:
Deep learning surrogate models have shown promise in solving partial differential equations. These efficient deep learning surrogate models enable many-query computations in science and engineering, in particular the engineering design optimization we focus on.
In this talk, I will first introduce a geometry-aware Fourier neural operator (Geo-FNO) to solve PDEs on arbitrary geometries, inspired by adaptive mesh motion and spectral methods. Furthermore, we study the cost-accuracy trade-off of different deep learning-based surrogate models, following traditional numerical error analysis, as the first step to building a complete theory of approximation error for these approaches. We demonstrate numerically the superior cost-accuracy trade-off of our approach. Finally, combining automatic differentiation tools of deep learning libraries, which efficiently compute gradients with respect to input variables enabling the use of gradient-based design optimization methods, our approach has demonstrated significant speed-up of airfoil design in transonic flow and real-world biomedical catheter design to prevent bacteria contamination.
（灰色区域内上下滑动阅读全部内容）
3. Weak convergence analysis of an explicit time-steppping fully discrete scheme for SPDEs with polynomialnonlinearity
报告人: 王小捷（中南大学）
报告时间: 2022-10.18 10:00-11:30
报告地点: 腾讯会议ID: 599 481 817
信息来源:
https://math.seu.edu.cn/2022/1013/c15556a423142/page.htm
报告摘要:
This talk is devoted to weak convergence analysis of an explicit full-discrete scheme for additive noise driven SPDEs with polynomialnonlinearity. A novel approach of weak convergence analysis is proposed and the expected weak convergence rates are successfully obtained for an explicit time-steppping fully discrete scheme. Numerical results are also provided to support our findings. This talk is based on a joint work with Siqing Gan and Meng Cai.
（灰色区域内上下滑动阅读全部内容）
4. Superconvergence of discontinuous Galerkin methods
信息来源:
http://www2.scut.edu.cn/math/2022/1012/c10160a483778/page.htm
5. 再探增广拉格朗日法
Speaker: 丁超（中国科学院数学与系统科学研究院应用数学研究所）
Time: 2022-10.19 14:00-15:30
Venue: Tencent Meeting ID: 332-470-708 Meeting Password: 221019
Info Source:
https://ins.sjtu.edu.cn/seminars/2167
Abstract:
自1969年由M.R. Hestenes和M.J.D. Powell提出以来，增广拉格朗日法以其深刻的优化理论以及求解优化问题时优异的数值效果，受到数学优化、机器学习等不同领域学者的广泛关注，并已被用于许多著名优化求解器以提高求解许多大规模约束优化问题的数值效果。在报告中，我们将结合矩阵优化最新理论结果，介绍增广拉格朗日法在求解非线性半正定优化、黎曼流形上的非光滑优化以及随机规划等问题的研究进展。
（灰色区域内上下滑动阅读全部内容）
6. Two-sample testing of high-dimensional linear regression coefficients via complementary sketching
报告人: 高凤楠（复旦大学）
报告时间: 2022-10.19 14:00-15:00
报告地点: 腾讯会议ID: 772-180-946
信息来源: https://www.math.sjtu.edu.cn/Default/seminarshow/tags/MDAwMDAwMDAwMLGelNyF2qF2
报告摘要:
We introduce a new method for two-sample testing of high-dimensional linear regression coefficients without assuming that those coefficients are individually estimable. The procedure works by first projecting the matrices of covariates and response vectors along directions that are complementary in sign in a subset of the coordinates, a process which we call 'complementary sketching'. The resulting projected covariates and responses are aggregated to form two test statistics, which are shown to have essentially optimal asymptotic power under a Gaussian design when the difference between the two regression coefficients is sparse and dense, respectively. Simulations confirm that our methods perform well in a broad class of settings, and an application to a large single-cell RNA sequencing dataset demonstrates its utility in the real world.
（灰色区域内上下滑动阅读全部内容）
7. Energy stable schemes for gradient flows based on the DVD method
报告人: 黄记祖（中国科学院数学与系统科学研究院）
报告时间: 2022-10.19 16:00-17:00
报告地点: 腾讯会议ID: 630111627 密码: 935570
信息来源: https://www.math.sjtu.edu.cn/Default/seminarshow/tags/MDAwMDAwMDAwMLGelN2FpKF2
报告摘要:
In this paper, we propose a new framework to construct energy stable scheme for gradient flows based on the discrete variational derivative method. Combined with the Runge--Kutta process, we can build an arbitrary high-order and unconditionally energy stable scheme based on the discrete variational derivative method. The new energy stable scheme is implicit and leads to a large sparse nonlinear algebraic system at each time step, which can be efficiently solved by using an inexact Newton type algorithm. To avoid solving nonlinear algebraic systems, we then present a relaxed discrete variational derivative method, which can construct linear unconditionally second-order energy stable schemes. Several numerical simulations are performed to investigate the efficiency, stability, and accuracy of the newly proposed schemes.
（灰色区域内上下滑动阅读全部内容）
8. Multiscale Finite Element Methods for advection-diffusion problems
信息来源:
https://hkumath.hku.hk/web/event/event-seminar.php
9. Convergence analysis of RBF contour integral methods forhigh-dimensional option pricing PDEs
报告人: 马敬堂（西南财经大学）
报告时间: 2022-10.20 19:30-21:00
报告地点: 腾讯会议ID: 806 176 595
信息来源:
https://math.seu.edu.cn/2022/1013/c15556a423145/page.htm
报告摘要:
In this talk, I present a hybrid method of radial basis functions semi-discretization and contour integral methods for solving high-dimensional partial differential equations (PDEs) arising in multi-assets options pricing. In the hybrid scheme, the PDEs are semi-discretized by the radial basis functions approximation for space and then the resulted ordinary differential equations are solved by the Laplace transform method which is regarded as the alternative of time-stepping. A fast contour integral method is developed to compute the inversion of Laplace transform. In the contour integral method, the inversion of Laplace transform is converted to a contour integral which can be computed efficiently by quadrature rules. The key point to the contour integral method is to design the contour which requires carefully analyzing the analytical region for the radial basis functions semi-discretization in the Laplace space. The spectral convergence rates of the approach are proved by analyzing the full errors from the radial basis functions semi-discretization and the numerical contour integrals. (This is joint work with Zhiqiang Zhou)
（灰色区域内上下滑动阅读全部内容）
我们是信息搬运工，
若活动临时有变化，
请以网站信息为准。
欢迎转发，点赞，在看。👇