Summary: Frontiers in the Theory and Application of Structure-Preserving Algorithms
The workshop "Frontiers in the Theory and Application of Structure-Preserving Algorithms," organized by Prof. Yajuan Sun (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China), Prof. Chaolong Jiang (Yunnan University of Finance and Economics, China), and Prof. Yushun Wang (Nanjing Normal University, China), was successfully held at the Tianyuan Mathematics Research Center, Kunming, from September 7 to 13, 2025.
This workshop aims to bring together international experts in structure-preserving algorithms to exchange insights on recent advances in the theory, development, and applications of structure-preserving numerical methods. Key topics include:
l Structure-preserving discretizations for partial differential equations (PDEs), such as curvature flows, nonlinear waves, complex fluids, and plasma physics etc.
l Stochastic methods and geometric integrators for stochastic systems.
l Low-rank approximation, model reduction, and parallel computing techniques that preserve geometric structures.
l Structure-preserving machine learning incorporating geometric constraints.
This workshop has gathered 31 participants from 20 universities and research institutes. Through the in-depth discussions on numerical methods and their applications, the event effectively facilitated high-quality collaborations and provided significant promotion for further development in the field of structure-preserving numerical methods.