Preprint

  1. Zhiqiang Cai, Yu Cao, Yuanfei Huang, and Xiang Zhou. Weak Generative Sampler to Efficiently Sample Invariant Distribution of Stochastic Differential Equation, 2024. [arXiv]

  2. Yu Cao, Shi Jin, and Nana Liu. Quantum simulation for time-dependent Hamiltonians–with applications to non-autonomous ordinary and partial differential equations, 2023. [arXiv]

  3. Yu Cao and Jianfeng Lu. Structure-preserving numerical schemes for Lindblad equations, 2021. [Code] [arXiv]

Publications

  1. Yu Cao, Jingrun Chen, Yixin Luo, and Xiang Zhou. Exploring the optimal choice for generative processes in diffusion models: Ordinary vs stochastic differential equations. Advances in Neural Information Processing Systems, 2023 [Code] [PDF]

  2. Yu Cao, Jianfeng Lu, and Lihan Wang. On explicit $L^2$-convergence rate estimate for underdamped Langevin dynamics. Arch Rational Mech Anal, 247(5), 2023 [DOI]

  3. Yu Cao and Eric Vanden-Eijnden. Learning optimal flows for non-equilibrium importance sampling. Advances in Neural Information Processing Systems, 2022 [Code] [PDF]

  4. Yu Cao, Jianfeng Lu, and Lihan Wang. Complexity of randomized algorithms for underdamped Langevin dynamics. Commun. Math. Sci., 19(7):1827–1853, 2021 [DOI]

  5. Yu Cao and Jianfeng Lu. Tensorization of the strong data processing inequality for quantum chi-square divergences. Quantum, 3:199, 2019 [DOI]

  6. Yu Cao, Jianfeng Lu, and Yulong Lu. Exponential decay of Rényi divergence under Fokker-Planck equations. J. Stat. Phys., 176(5):1172–1184, 2019 [DOI]

  7. Yu Cao, Jianfeng Lu, and Yulong Lu. Gradient flow structure and exponential decay of the sandwiched Rényi di vergence for primitive Lindblad equations with GNS-detailed balance. J. Math. Phys., 60(5):052202, 2019 [DOI]

  8. Yu Cao and Jianfeng Lu. Stochastic dynamical low-rank approximation method. J. Comput. Phys., 372:564–586, 2018 [DOI]

  9. Yu Cao and Jianfeng Lu. Lindblad equation and its semiclassical limit of the Anderson-Holstein model. J. Math. Phys., 58(12):122105, 2017 [DOI]

  10. Yu Cao, Ling Lin, and Xiang Zhou. Explore stochastic instabilities of periodic points by transition path theory. J. Nonlinear Sci., 26(3):755–786, 2016 [DOI]