題目：Characteristic-featured troubled-cell indicator for Conservation Laws based on Artificial Neural Network
報告人：劉鐵鋼教授（北京航空航天大學數學科學學院）
邀請人：沈曉芹教授（理學院數學係）
報告時間：2023年4月16日下午3:00-4:30
報告地點：教九樓理學院會議室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.
報告人簡介：劉鐵鋼，北京航空航天大學數學科學學院教授，研究生院副院長兼培養處處長，教育部“數學、信息與行為”重點實驗室主任。主要研究方向為可壓縮多介質流體數值方法、氣動優化與設計、空化流建模及數值模擬、爆炸衝擊中流-固耦合及動邊界問題數值模擬等。曾任中國數學學會理事，中國工業與應用數學學會常務理事，中國計算數學學會常務理事，教育部高等教育數學類專業教學指導委員會秘書長；現任北京市計算數學學會常務理事，《計算數學》等期刊編委。
