Claire Valva

I am postdoc at Caltech in the department of Computing + Mathematical Sciences working with Andrew Stuart. I received my PhD in May 2025 from the Center for Atmosphere and Ocean Science at the Courant Institute of Mathematical Sciences where I was advised by Dimitris Giannakis and Ed Gerber.

My research asks how useful structure can be extracted from complex dynamical systems and when such structure can (and cannot) be used to construct reliable data-driven models. I combine dynamical systems theory with modern computational methods to understand system dynamics, improve prediction, and characterize the reliability of data-driven models. In particular, I am interested in applications of these methods for the understanding and prediction of weather and climate.

Publications

  • Learning Kolmogorov Backward Operators for Spectral Analysis and Forecasting: A Data-Driven Variational Galerkin Framework with Yuanchao Xu, Ben Gao, and Isao Ishikawa, arXiv.
  • A more predictable Madden-Julian Oscillation index derived from Koopman spectral analysis with Edwin P Gerber, arXiv.
  • Physics-informed spectral approximation of Koopman operators with Dimitris Giannakis, paper.
  • The QBO, the annual cycle, and their interactions: Isolating periodic modes with Koopman analysis with Edwin P Gerber, paper.
  • Consistent spectral approximation of Koopman operators using resolvent compactification with Dimitris Giannakis, paper
  • Koopman analysis of the periodic Korteweg–de Vries equation with Jeremy Parker, paper.
  • What Controls the Probability Distribution of Local Wave Activity in the Midlatitudes? with Noboru Nakamura, paper.

    • CV   Google Scholar   GitHub  ORCID
     
    Annenberg Center for Information Science and Technology
    California Institute of Technology

    clairev (at) caltech.edu