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报告时间：2025年7月22日下午15:00
报告地点：红瓦楼826
报告一题目: Hyperbolic Inverse Problems and NN
报告人：Sergey Kabanikhin 俄罗斯科学院通讯院士，俄罗斯科学院西伯利亚分院索伯列夫数学研究所国际数学中心主任
报告一内容简介：Hyperbolic inverse problems involve recovering unknown parameters or conditions from observed data governed by hyperbolic PDEs, such as the wave equation. These problems frequently arise in geophysics, medical imaging, and acoustics and are typically ill-posed, making solutions sensitive to data perturbations. Neural networks offer promising solutions due to their capability to approximate complex functions and manage noisy data effectively. They inherently include regularization through their architecture, stabilizing the solutions. Generative Adversarial Networks (GANs) help generate synthetic data, particularly useful when real observational data is limited. Neural networks also efficiently model forward mappings, facilitating computationally effective inversion, and quantify uncertainties, providing confidence intervals for the solutions. However, challenges like extensive data requirements, risk of overfitting, and limited interpretability remain. This talk aims to enhance robustness, interpretability, and computational efficiency, underscoring the potential of neural networks for practical hyperbolic inverse problem applications.
报告人简介：谢尔盖·卡巴尼欣（Sergey I. Kabanikhin），俄罗斯科学院通讯院士，俄罗斯科学院西伯利亚分院索伯列夫数学研究所国际数学中心主任，2015-2018曾任俄罗斯科学院西伯利亚分院计算数学与数学地球物理研究所（ICM&MG SB RAS）所长; ICM&MG SB RAS地球物理数学实验室主要研究员， 新西伯利亚国立大学数力系地球物理数学方法教研室主任。S.I.Kabanikhin现为俄罗斯科学院西伯利亚分院索博列夫数学研究所、计算数学与数学地球物理研究所以及新西伯利亚国立大学数力系学术委员会委员，ICM&MG SB RAS研究所博士论文答辩委员会主席，俄罗斯科学院数学科学办公室成员，俄罗斯科学院西伯利亚分院主席团成员. S.I. Kabanikhin已发表超过200篇论文，出版学术著作15部。其中专著《Inverse and Ill-Posed Problems》于2008年被索博列夫数学研究所评为最佳出版物，并进入俄罗斯科学院西伯利亚分院出版的14本最佳图书名单（2009年）。S.I.Kabanikhin培养了许多年轻科学家。他的八名学生完成了科学博士答辩，二十四名学生完成了副博士（PhD）答辩。
报告二题目：Inverse problems for parabolic equations in finance and medicine
报告人：Maxim Shishlenin 俄罗斯科学院教授、俄罗斯科学院西伯利亚分院索伯列夫数学研究所、计算数学和数学地球物理学研究所首席研究员
报告二内容简介：In the talk the inverse problems for parabolic equations that arise in applications such as financial mathematics and drug assimilation are investigated. We will consider the formulation of inverse problems of determining the coefficients, depending on time or spatial variables, based on data given in a discrete set of points and on a curve inside the region.
报告人简介：Professor of the Russian Academy of Sciences (elected 2022) and Leading Researcher at Sobolev Institute of Mathematics and at the Institute of Computational Mathematics and Mathematical Geophysics (Novosibirsk). He served Deputy Director for Science at the Institute of Computational Mathematics and Mathematical Geophysics in 2016-2019 and Sobolev Institute of Mathematics in 2021-2024. His research specializes in inverse and ill-posed problems of mathematical physics, particularly numerical methods for PDEs with application to acoustic, seismic, electromagnetic and social-economical processes. He co-authored foundational texts on computational methods for inverse problems and published extensively in Q1 journals (e.g., Journal of Inverse and Ill-Posed Problems, Advances in Computational Mathematics, PLOS One, Scientific Reports). A recipient of the Young Scientist Award in Inverse Problems (2008), he organizes major international conferences and serves as Managing Editor for Journal of Inverse and Ill-Posed Problems. He holds a Dr.Sc. (2016) and Ph.D. (2003) under Sergey Kabanikhin, and teaches at Novosibirsk State University since 2000.
报告邀请人：徐定华