报告题目1：Robust Full Waveform Inversion: A Source Wavelet Manipulation Perspective

报告人：邱凌云，清华大学丘成桐数学中心

报告时间：2023年6月22日8:30

报告地点：20幢404（第一会议室）

报告摘要：Full-waveform inversion (FWI) is a powerful tool for high-resolution subsurface parameter reconstruction. Due to the existence of local minimum traps, the success of the inversion process usually requires a good initial model. Our study primarily focuses on understanding the impact of source wavelets on the landscape of the corresponding optimization problem. We thus introduce a decomposition scheme that divides the inverse problem into two parts. The first step transforms the measured data into data associated with the desired source wavelet. Here, we consider inversions with known and unknown sources to mimic real scenarios. The second sub-problem is the conventional full waveform inversion, which is much less dependent on an accurate initial model since the previous step improves the misfit landscape. A regularized deconvolution method and a convolutional neural network are employed to solve the source transformation problem. Numerical experiments on the benchmark models demonstrate that our approach improves the gradient's quality in the subsequent FWI and provides a better inversion performance.

报告人简介：邱凌云，现任清华大学丘成桐数学科学中心特别研究员、博导，于2013年在美国普渡大学数学系获得博士学位。在加入清华大学之前，其曾在2015年至2018年就职于PGS (Petroleum Geo-Services)位于美国休斯敦的全球研发总部，从事地震波反演问题的研究工作。2013年至2015年，邱凌云博士在明尼苏达大学的IMA(Institute for Mathematics and its Applications)和埃克森美孚位于美国新泽西州的研究与工程中心(ExxonMobil’s Research and Engineering Technology Center)担任联合职位博士后。邱博士的主要研究兴趣包括非线性反问题的分析与计算、最优输运理论、正则化方法、最优化问题的迭代算法以及深度学习在反问题上的应用。

报告题目2：High order bound preserving methods for compressible multi-species flow with chemical reactions

报告人：杜洁，清华大学丘成桐数学中心

报告时间：2023年6月22日9:20

报告地点：20幢404（第一会议室）

报告摘要：In this talk, we develop third-order conservative sign-preserving and steady-state preserving time integrations and seek their applications in multispecies and multireaction chemical reactive flows. In this problem, the density and pressure are nonnegative, and the mass fraction should be between 0 and 1. There are four main difficulties in constructing high-order bound-preserving techniques for multispecies and multireaction detonations. First of all, most of the bound-preserving techniques available are based on Euler forward time integration. Therefore, for problems with stiff source, the time step will be significantly limited. Secondly, the mass fraction does not satisfy a maximum principle and hence it is not easy to preserve the upper bound 1. Thirdly, in most of the previous works for gaseous denotation, the algorithm relies on second-order Strang splitting methods where the flux and stiff source terms can be solved separately, and the extension to high-order time discretization seems to be complicated. Finally, most of the previous ODE solvers for stiff problems cannot preserve the total mass and the positivity of the numerical approximations at the same time. In this work, we will construct third order conservative sign-preserving Rugne-Kutta and multistep methods to overcome all these difficulties. The time integrations do not depend on the Strang splitting, i.e. we do not split the flux and the stiff source terms. Moreover, the time discretization can handle the stiff source with large time step and preserves the steady-state. Numerical experiments will be given to demonstrate the good performance of the bound-preserving technique and the stability of the scheme for problems with stiff source terms.

报告人简介：杜洁，清华大学丘成桐数学科学中心助理教授，博士生导师。2010年进入中国科学技术大学数学科学学院攻读博士学位，期间多次前往香港大学担任研究助理。2014年作为国家公派联合培养博士研究生前往布朗大学数学系学习。2015年进入香港中文大学数学系做博士后。2017年就职于清华大学。多年来从事偏微分方程高精度数值算法及计算流体力学的研究，并在应用层面研究交通流问题的建模和数值模拟。于数值计算及其应用方向的主流杂志上已发表了20余篇学术论文，其中包括应用数学类著名杂志SIAM Journal on Scientific Computing和Journal of Computational Physics以及工程类顶级期刊Transportation Research Part B等。

报告题目3：Traceability of Water Pollution: An Inversion Scheme Via Dynamic CGO Solutions

报告人：蔚辉，清华大学丘成桐数学中心

报告时间：2023年6月22日10:10

报告地点：20幢404（第一会议室）

报告摘要：We aim to find the time-dependent source term in the diffusion equation from the boundary measurement, which allows for the possibility of tracing back the source of pollutants in the environment. Based on the idea of dynamic complex geometrical optics (CGO) solutions, we analyze a variational formulation of the inverse source problem and prove the uniqueness result. A two-step reconstruction algorithm is proposed, which first recovers the locations of the point sources, and then the Fourier components of the emission concentration functions are reconstructed. Numerical experiments on simulated data are conducted. The results demonstrate that our proposed two-step reconstruction algorithm can reliably reconstruct multiple point sources and accurately reconstruct the emission concentration functions. In addition, we decompose the algorithm into two parts: online and offline computation, with most of the work done offline. This paves the way toward real-time traceability of the pollution. The proposed method can be used in many fields, particularly those related to water pollution, to identify the source of a contaminant in the environment and can be a valuable tool in protecting the environment.

报告题目4：Stochastic algebraic Riccati equations are almost as easy as deterministic ones

报告人：梁鑫，清华大学丘成桐数学中心

报告时间：2023年6月22日11:00

报告地点：20幢404（第一会议室）

报告摘要：Stochastic algebraic Riccati equations, also known as rational algebraic Riccati equations, arising from stochastic optim al control, were considered to be not easy to solve. The-state-of-art numerical methods most rely on differetiability or continuity, such as Newton-type method or homotopy method. In this talk, we will build a novel theoretical framework and reveal the intrinsic algebraic structure appearing in this kind of algebraic Riccati equations. This structure guarantees that to solve it is almost as easy as a deterministic/classical one, which will shed light on the theoretical analysis and numerical algorithm design. This is a joint work with Zhen-Chen Guo (Nanjing University).