汇报标题 (Title)：Continual learning for Least square collocation methods for PDEs（最幼二乘配点法求解偏微分方程的持续进建战术）
汇报人 (Speaker)：张中强 教授（Worcester Polytechnic Institute）
汇报功夫 (Time)：2026年6月18日(周四) 15:00
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：李常品、蔡敏
主办部门：理学院数学系
汇报提要：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.
