报告人：程自强

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

时间：2026年5月28日 10:00–12:00

地点：数学楼 2-2

报告摘要：

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 interpretation 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，博士，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 Journal of Computational Physics、Journal of Computational and Applied Mathematics、Communications in Nonlinear Science and Numerical Simulation、Journal of Theoretical Biology、Journal of Scientific Computing 等国际期刊上发表论文10余篇。