报告题目：Learning Explicit Symbolic Smoothness Indicators for WENO Schemes via Kolmogorov–Arnold Networks

报告人：程自强

报告时间：2026年9月28日下午，3:30-4:30

地点：管理科研楼1218室

摘要：

This work introduces an interpretable, KAN-based framework to learn data-driven $\beta$-type smoothness indicators for WENO schemes. Unlike typical black-box MLPs, the structural interpretability of KANs allows the trained network to be converted into explicit closed-form analytical formulas. Consequently, the new indicators can be coded directly into standard solvers, eliminating runtime neural-network inference overhead. While preserving the classical WENO weighting architecture, numerical simulations for hyperbolic conservation laws show that the proposed scheme achieves sharper shock resolution and superior accuracy compared to WENO-Z and WENO-NN. Furthermore, it significantly outperforms WENO-NN in computational speed, offering a robust and efficient approach to enhancing high-order shock-capturing methods via symbolic learning.

报告人简介：

程自强，合肥工业大学数学学院副教授。主要从事偏微分方程数值方法和生物模型的研究工作。主持或参与国家级科研项目，在J. Comput. Phys., J. Comput. Appl. Math., Commun. Nonlinear Sci. Numer. Simul., J. Theor. Biol., J. Sci. Comput.等国际期刊上发表论文10余篇。