報告題目：Transformer Meets Boundary Value Inverse Problems
報 告 人：Long Chen 教授
所在單位：University of California at Irvine (UCI)
報告時間：2022年11月04日 星期五 上午11:00
報告地點：#騰訊會議：108 807 618
校内聯系人：賈繼偉 jiajiwei@jlu.edu.cn
報告摘要： A Transformer-based deep direct sampling method is proposed for solving a class of boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and the reconstructed images. An effort is made to give a specific example to a fundamental but critical question: whether and how one can benefit from the theoretical structure of a mathematical problem to develop task-oriented and structure-conforming deep neural network? Specifically, inspired by direct sampling methods for inverse problems, the 1D boundary data are preprocessed by a partial differential equation-based feature map to yield 2D harmonic extensions in different frequencies as different input channels. Then, by introducing learnable non-local kernel, the approximation of direct sampling is recast to a modified attention mechanism. The proposed method is then applied to electrical impedance tomography, a well-known severely ill-posed nonlinear inverse problem. The new method achieves superior accuracy over its predecessors and contemporary operator learners, as well as shows robustness with respect to noise.
This research shall strengthen the insights that the attention mechanism, despite being invented for natural language processing tasks, offers great flexibility to be modified in conformity with the a priori mathematical knowledge, which ultimately leads to the design of more physics-compatible neural architectures.
This is a joint work with Ruchi Guo (UCI) and Shuhao Cao (University of Missouri-Kansas City).
報告人簡介：陳龍目前是加州大學歐文分校（UCI）的數學教授。 1997年畢業于南京大學，2000年獲北京大學碩士學位，2005年獲賓夕法尼亞州立大學博士學位。博士生導師為許進超教授。 2005年至2007年在加州大學聖地亞哥分校和馬裡蘭大學帕克分校從事博士後研究。 2007年起在UCI工作，2011年獲得終身教職，2015年晉升為正教授。
陳教授的研究領域是偏微分方程的數值解，尤其是有限元方法的設計與分析。此外，陳教授還開發了iFEM有限元軟件包，為有限元方法的教學和研究提供了極大的便利。陳教授在國際知名期刊發表學術論文60餘篇，擔任多個SCI期刊編委。
更多詳情請訪問陳教授網站：https://www.math.uci.edu/~chenlong/。
