SKDMD

Sparsity-promoting Kernel Dynamic Mode Decomposition

Motivations

Why throwing everything in a neural network?
- neural network approach for finding Koopman operators could suffer from bad minimizers, time consuming (requires an unknown number of GPU training hours), which are all resulted from the non-convex optimization nature
Why not using classical convex methods?
- classical nonlinear Koopman analysis method (e.g., EDMD, KDMD) suffers from having hundreds to thousands of approximated Koopman triplets.
- How to choose an accurate and informative Koopman invariant subspace in Extended/Kernel DMD?
Not every nonlinear dynamical system requires a neural network to search for Koopman operator
- we resolve the issue of classical methods by rethinking modes selection in EDMD/KDMD as a multi-task learning problem
- demonstration on several strongly transient flows shows the effectiveness of the algorithm for providing an accurate reduced-order-model (ROM)

go to EXAMPLE/cylinder_re100 folder
run a standard KDMD
- python3 example_20d_cyd.py
perform multi-task learning mode selection
- note that in run_apo_cyd_ekdmd.py, themax_iter = 1e5 iis a safe choice for getting accurate result, one can choose max_iter=1e3 to just get a try of the algorithm
- python3 run_apo_cyd_ekdmd.py
postprocessing the result of multi-task learning
- python3 pps_cyd.py
Note: that the data is top 20 POD coefficients with mean-subtracted.

go to EXAMPLE/cylinder_re100/hyp
run parallem hyperparameter selection
- python3 cv_kdmd_hyp_20d_cyd.py
then collecting the result and draw the figure by
- python3 print.py
the resulting figure result-num.png is a good refernce of choosing hyperparameter