AM Seminar: Discovering governing equations from data using sparse identification and deep learning methods

Speaker: 

Joseph Bakarji, Postdoctoral Fellow, AI Institute in Dynamic Systems, University of Washington

Description:

 Recent advancements in machine learning have revolutionized computational solvers and enabled data-driven discovery in complex systems. However, combining available data with known physical laws to maximize
generalization and guarantee robustness remains a significant challenge. I will present our latest work that addresses this challenge using deep learning and sparse identification methods. First, I will demonstrate how
probability distribution function equations can be inferred from Monte Carlo simulations for the purpose of coarse-graining and closure modeling. Second, I will present three methods for discovering dimensionless groups from data using the Buckingham Pi theorem as a constraint. Third, I will discuss the deep delay autoencoder algorithm, which reconstructs high-dimensional systems of differential equations from partial measurements, as motivated by Takens' theorem. Finally, I will highlight the limitations of these methods and suggest potential avenues for future
research.