Past Event: Oden Institute Seminar

How much can we learn from empirical data?

Brendan Keith, Postdoctoral Researcher, Lawrence Livermore National Laboratory

Abstract

Classical physical theories begin with scientific laws as ansätze which are validated by repeated scientific experiment. From these laws, one derives a set of equations (usually differential equations) which can be solved to make predictions about the physical system under consideration. Physical theories, and the mathematical models they deliver, provide useful but idealized perspectives of physical processes. Experimental measurements complement this perspective by providing direct observation data for particular physical processes. However, these data are typically not complete enough to uniquely and entirely characterize any one process.
    
    Incorporating experimental measurements into mathematical models allows us to assimilate latent information into a simulation environment that cannot be extracted from first principles alone. In engineering, this procedure has long been called "model calibration" but has taken on new prominence in the age of scientific machine learning.
    
    In this talk we codify two recent contributions in what may be seen as advanced model calibration or "model discovery". In the first contribution, we consider the dynamics of binary black hole systems. Here, we introduce "gravitational waveform inversion" which allows us to "discover" unique dynamical models of relativistic mechanics from only a single time series of (possibly noisy) waveform data. In the second contribution, we consider neutrally stable turbulent flow in the atmospheric boundary layer (Re ~ 10^6 - 10^8). Here, we introduce a kernel regression problem which allows us to learn mass-conserving, nonlocal, anisotropic synthetic turbulence models from incomplete and noisy field measurements.
    
    The topics in this presentation feature joint work with Scott Field, Akshay Khadse, Ustim Khristenko, and Barbara Wohlmuth. If time permits, additional topics will be discussed, including ongoing work on reinforcement learning for optimization of dynamic processes and simulation.
    

 

Biography

Brendan Keith, Postdoctoral Researcher at Lawrence Livermore National Laboratory, is a Canadian mathematician and computational scientist. He received his Ph.D. from the Oden Institute for Computational Engineering and Sciences in August 2018, under the supervision of Leszek Demkowicz. His main research contributions are in the development and analysis of finite element methods, especially the DPG method. More recently, he has contributed to the fields of stochastic optimization, uncertainty quantification, fractional PDEs, and scientific machine learning.