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

Stacks Image 7


[ View ]

Learning Flow Maps with Neural Networks

Stacks Image 16


[ View ]


Multiscale Flow Maps

Stacks Image 26


[ View ]



Supplementary Videos


Stacks Image 61
This video details the hierarchical time-stepping algorithm learned by neural networks [ VIEW ]