This talk will present a hybrid quantum–classical reduced-order modeling (ROM) framework for unsteady fluid flows. It is based on variational quantum singular value decomposition (VQSVD) and a linear-layer enhanced quantum long short-term memory network (L-QLSTM). The proposed architecture first applies VQSVD to compress high-dimensional flow fields into a low-dimensional latent representation parameterized by reduced coefficients. The temporal fluid dynamics evolution of these coefficients is then learnt using L-QLSTM, which maps past coefficients to the next-step coefficients through variational quantum circuits with entangling layers and linear projections. The convergence of VQSVD under finite-shot stochastic gradients induced by parameter-shift measurements is analyzed. Furthermore, Lipschitz stability for L-QLSTM is established, and a multistep inference error bound accounting for VQSVD noise and model approximation is obtained. Finally, the predicted coefficients are lifted back to the full state space using the VQSVD modes. Two Numerical experiments: flow past a cylinder and flow past two cylinders demonstrate that the proposed quantum ROM achieves faster convergence and improved long-horizon stability compared with the classical ROM.

报告人简介：肖敦辉，同济大学数学科学学院教授，国家高层次海外青年人才。入选全球2%顶尖科学家，应用数学类排名全球290. 计算数学教研室主任、中国数学会计算数学分会常务理事、中国空气动力学会智能流体力学专委会委员、中国岩石力学与工程协会AI实用化学会常务委员、上海CSIAM委员、张江数学研究院同济分院负责人。于2013年获帝国理工全奖开始攻读计算流体力学博士，于2016年获博士学位，并且获帝国理工最佳科研博士生奖，一年一个。之后在帝国理工地球科学系和数据科学所从事博士后研究。后加入号称有限元发源地之一的斯旺西大学辛克维奇工程计算中心从事科研和教学工作，担任讲师和博士生导师。主持的项目包括英国基金委如EPSRC和Royal Society项目以及NSFC面上以及青年等项目。在SIAM journal on scientific computing、JCP、CMAME、IJNME等期刊发表模型降阶理论和应用方面论文60多篇。担任英国EPSRC、欧洲ERC，Nature子刊和国内各基金等评审专家。

注：本报告由数学科学全国重点实验室开放课题SLMS-2025-KFKT-TD-11组织。