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题    目：Structure-Preserving Methods for Linearly Perturbed Hamiltonian Systems: From Energy-Stable Integrators to Conformal-Symplectic Learning

主讲人：李露 副教授

单    位：中山大学

时    间：2026年7月10日 10:30

地    点：郑州校区九章学堂南楼C座209

摘    要：Dissipative Hamiltonian systems arise in mechanical vibrations, dispersive models, and many complex physical systems. This talk presents an energy-stable splitting exponential integration framework for linearly perturbed Hamiltonian systems. By reinterpreting SAV and its Lagrange-multiplier variant from a Poisson-system viewpoint and coupling the resulting Hamiltonian subsolvers with the exact damping subflow, we obtain two schemes: SEISAV, which ensures modified-energy dissipation with only a scalar linear algebraic solve, and SEILM, which enforces original-energy dissipation through a scalar nonlinear constraint. We also briefly discuss CSympNet-ID, a conformal-symplectic map-learning extension for learning one-step maps and identifying damping factors from snapshot data.

简    介：李露，2024年入职中山大学数学学院（珠海），于2019年10月获挪威科技大学哲学博士学位， 师从Elena Celledoni教授, 2015年获中国科学院大学硕士学位，师从尚在久研究员。研究领域包括微分方程保结构算法，机器学习及其应用，在SIAM Journal on Scientific Computing, Journal of Computational Physics 以及 BMC Bioinformatics, Metabolomics 等杂志发表多篇论文，主持国家自然科学基金青年基金C类一项，参与国家自然科学基金重点项目一项。