Sparse Nonlinear Models for Fluid Dynamics with Machine Learning and Optimization

Explore the application of sparse identification of nonlinear dynamics (SINDy) algorithm in developing reduced-order models for complex fluid flows. Delve into recent innovations in modeling various flow fields, including bluff body wakes, cavity flows, thermal and electro convection, and magnetohydrodynamics. Learn about the balance between accuracy and efficiency in these models, essential for real-time control, prediction, and optimization of engineering systems involving working fluids. Examine the integration of SINDy with deep autoencoders, Galerkin regression, and stochastic modeling for turbulence. Discover how these techniques are applied to interpret and generalize machine learning in fluid dynamics, from partial differential equation discovery to dominant balance physics modeling.

Introduction.
Interpretable and Generalizable Machine Learning.
SINDy Overview.
Discovering Partial Differential Equations.
Deep Autoencoder Coordinates.
Modeling Fluid Flows with Galerkin Regression.
Chaotic thermo syphon.
Chaotic electroconvection.
Magnetohydrodynamics.
Nonlinear correlations.
Stochastic SINDy models for turbulence.
Dominant balance physics modeling.