Publications

Preprints

• PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

  Yuxuan Liu, Jingmin Sun, Xinjie He, Griffin Pinney, Zecheng Zhang, and Hayden Schaeffer.
  arXiv preprint arXiv:2409.09811, 2024. [code]

• Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey

  Haixin Wang, Yadi Cao, Zijie Huang, Yuxuan Liu, Peiyan Hu, Xiao Luo, Zezheng Song, Wanjia Zhao, Jilin Liu, Jinan Sun, Shikun Zhang, Long Wei, Yue Wang, Tailin Wu, Zhi-Ming Ma, and Yizhou Sun.
  arXiv preprint arXiv:2408.12171, 2024.

• Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation

  Jingmin Sun, Yuxuan Liu, Zecheng Zhang, and Hayden Schaeffer.
  arXiv preprint arXiv:2404.12355, 2024. [code]

Journal Papers

• PROSE: Predicting Multiple Operators and Symbolic Expressions using Multimodal Transformers

  Yuxuan Liu, Zecheng Zhang, and Hayden Schaeffer.
  Neural Networks, 106707, 2024. [code]

• Random Feature Models for Learning Interacting Dynamical Systems

  Yuxuan Liu, Scott G. McCalla, and Hayden Schaeffer.
  Proceedings of the Royal Society A 479 (2275), 20220835, 2023. [code]

• Surfactant Dynamics from the Arnold Perspective

  J. Jenkins, C. Lee, Y. Liu, E. Lu, and D. Reed.
  SIAM Undergraduate Research Online 14, 2021.