About Me

Symmetry-reduced model reduction for shift-equivariant systems

We develop data-driven reduced-order models of partial differential equations with shift symmetry (also called shift equivariance). Such systems typically admit traveling solutions, which require many basis functions in a fixed reference frame. We instead represent the solution in a traveling reference frame, thereby obtaining a more compact representation. Existing methods such as operator inference then fit the reduced model directly from data, without knowledge of the full-order dynamics.

We are now developing a joint optimization that learns the projection subspaces and the symmetry-reduced dynamics together.

• Symmetry-reduced model reduction of shift-equivariant systems via operator inference
  Yu Shuai and Clarence W. Rowley
  Advances in Computational MathematicsUnder revision
  arXiv:2507.18780, 2025.
  [arXiv][PDF][Code]
  BibTeX

  @misc{shuai2025symmetryreduced,
    title = {Symmetry-reduced model reduction of shift-equivariant systems via operator inference},
    author = {Shuai, Yu and Rowley, Clarence W.},
    year = {2025},
    eprint = {2507.18780},
    archivePrefix = {arXiv},
    primaryClass = {math.NA},
    url = {https://arxiv.org/abs/2507.18780}
  }

Detecting Lagrangian coherent structures from sparse data

We are investigating flow reconstruction and Lagrangian coherent-structure analysis from sparse tracer measurements in the atmospheric surface layer, with attention to the limitations imposed by finite observations.

Sparse observations · flow reconstruction · Lagrangian analysis · no paper yet

Structured input–output analysis of wall-bounded shear flows

We studied the amplification and characteristic scales of oblique laminar–turbulent patterns in plane Couette–Poiseuille flow using structured input–output analysis.

• Structured input–output analysis of oblique laminar–turbulent patterns in plane Couette–Poiseuille flow
  Yu Shuai, Chang Liu, and Dennice F. Gayme
  International Journal of Heat and Fluid Flow, 103, 109207, 2023.
  [Publisher]
  BibTeX

  @article{shuai2023structured,
    title = {Structured input-output analysis of oblique laminar-turbulent patterns in plane Couette-Poiseuille flow},
    author = {Shuai, Yu and Liu, Chang and Gayme, Dennice F.},
    journal = {International Journal of Heat and Fluid Flow},
    volume = {103},
    pages = {109207},
    year = {2023},
    doi = {10.1016/j.ijheatfluidflow.2023.109207}
  }

• A structured input-output approach to characterizing optimal perturbations in wall-bounded shear flows
  Chang Liu, Yu Shuai, Aishwarya Rath, and Dennice F. Gayme
  2023 American Control Conference (ACC), pp. 2319–2325, 2023.
  [Publisher][arXiv][PDF]
• Structured input-output analysis of oblique turbulent bands in transitional plane Couette-Poiseuille flow
  Yu Shuai, Chang Liu, and Dennice F. Gayme
  Proceedings of the 12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12), Osaka, Japan, 2022.
  [Proceedings PDF]