j9九游会

报告问题 (Title)：Continual learning for Least square collocation methods for PDEs（最小二乘配点法求解偏微分方程的持续学习战略）

报告人 (Speaker)：张中强 教授（Worcester Polytechnic Institute）

报告时间 (Time)：2026年6月18日(周四) 15:00

报告所在 (Place)：校本部GJ303

约请人(Inviter)：李常品、蔡敏

主理部分：理学院数学系

报告摘要：A least squares collocation method is presented for stiff PDEs with small parameters. By embedding these parameters directly into the formulation, the scheme resolves sharp gradients without auxiliary basis enrichment or parameter tuning. The method follows a continuation path—starting from larger parameter values and gradually approaching the target—to enhance stability in highly stiff regimes. Minimizing the residual at collocation points yields a compact, robust approach for capturing large derivatives. Numerical tests verify its accuracy, and the same framework extends naturally to optimal control problems through least squares enforcement of state and optimality conditions.