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[00975] Data-driven methods for learning mathematical models

  • Session Date & Time : 5D (Aug.25, 15:30-17:10)
  • Type : Proposal of Minisymposium
  • Abstract : Mathematical models are important tools helping people understand scientific phenomena in many disciplines. Recent advances in technologies make it easier to collect huge amounts of data, which offers new opportunities on data-driven methods for the identification of mathematical models behind a phenomenon. This minisymposium focuses on learning mathematical models from an observed data set. Topics in this field include identification of governing equations, reconstruction of certain functions in an equation, and learning operators between input and output spaces. Recently, there have been interesting developments in this field, varying from problem formulations, efficient solvers, techniques on improving robustness to theoretical analysis. This minisymposium brings together researchers to discuss recent advances, challenges and applications in this field.
  • Organizer(s) : Yuchen He, Hao Liu
  • Classification : 35RXX, 65ZXX, 37MXX, 65MXX, differential equation and operator learning
  • Speakers Info :
    • Yuchen He (Shanghai Jiao Tong University)
    • David Bortz (University of Colorado Boulder)
    • Yimin Zhong (Auburn University)
    • Bethany Lusch (Argonne National Lab)
  • Talks in Minisymposium :
    • [05246] Learning Koopman Operators that Generalize Well
      • Author(s) :
        • Bethany Lusch (Argonne National Laboratory)
      • Abstract : The Koopman operator is a way to represent a nonlinear dynamical system as a globally linear system. However, the linear system is infinite-dimensional, and the representation is difficult to find. Much recent research is on data-driven methods to approximate the Koopman operator. However, finding an approximation that generalizes well for a large region without finely sampling the space can be challenging. We explore learning a Koopman operator that can generalize well given limited data.