Publications

Preprints

• A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptions

  Elisa Negrini, Yuxuan Liu, Liu Yang, Stanley Osher, and Hayden Schaeffer.
  arXiv preprint arXiv:2502.06026, 2025.

• BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics

  Yuxuan Liu, Jingmin Sun, and Hayden Schaeffer.
  arXiv preprint arXiv:2501.18972, 2025. [code]

• VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction

  Yadi Cao*, Yuxuan Liu*, Liu Yang, Rose Yu, Hayden Schaeffer, and Stanley Osher.
  arXiv preprint arXiv:2411.16063, 2024.

• 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.
  NeurIPS 2024 Foundation Models for Science Workshop, 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.

Journal Papers

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

  Jingmin Sun, Yuxuan Liu, Zecheng Zhang, and Hayden Schaeffer.
  To appear in Physics Review E, 2024. [code]

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

  Yuxuan Liu, Zecheng Zhang, and Hayden Schaeffer.
  Neural Networks, 180:106707, 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.