题目：Characteristic-featured troubled-cell indicator for Conservation Laws based on Artificial Neural Network
报告人：刘铁钢教授（北京航空航天大学数学科学学院）
邀请人：沈晓芹教授（理学院数学系）
报告时间：2023年4月16日下午3:00-4:30
报告地点：教九楼理学院会议室9-320
摘要:We use exact solutions of one-dimensional Burgers equation to train an artificial neural network as a shock wave detector. The expression of the artificial neuron detector is then modified into a practical form to reflect admissible jump of eigenvalues. We show the working mechanism of the practical form is consistent with compressing or intersecting of characteristic curves. We prove there is indeed a discontinuity inside the cell detected by the practical form, and smooth extrema and large gradient regions are never marked. This indicator can be easily extended to multi-dimensional conservation laws without retraining. Numerical results are present to demonstrate the robustness of the present indicator under Runge-Kutta Discontinuous Galerkin framework, its performance is generally compared to TVB-based indicators more efficiently and accurately. This is a joint work with Yiwei Feng and Kun Wang.
报告人简介：刘铁钢，北京航空航天大学数学科学学院教授，研究生院副院长兼培养处处长，教育部“数学、信息与行为”重点实验室主任。主要研究方向为可压缩多介质流体数值方法、气动优化与设计、空化流建模及数值模拟、爆炸冲击中流-固耦合及动边界问题数值模拟等。曾任中国数学学会理事，中国工业与应用数学学会常务理事，中国计算数学学会常务理事，教育部高等教育数学类专业教学指导委员会秘书长；现任北京市计算数学学会常务理事，《计算数学》等期刊编委。
