Machine Learning, Dynamical Systems and Control

Time-stepping algorithms are critical for modeling systems that evolve in time. Fluid flows are typically spatio-temporal systems whose temporal evolution is dominated by nonlinear processes. In these lectures, we use neural networks to construct flow maps that characterise the evolution dynamics over a prescribed time increment. We further connect flow maps to standard numerical solvers such as Euler and Runge-Kutta steppers.

 

Jupyter notebook

 

Time-Stepping and Flow Maps

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[ View ]

Learning Flow Maps with Neural Networks

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Multiscale Flow Maps

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[ View ]

 

 

Supplementary Videos

 

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This video details the hierarchical time-stepping algorithm learned by neural networks [ VIEW ]