Outline
00:00 - Intro
01:15 - Origin story: early path and the road to science
04:20 - On graphical visualization and aphantasia
08:08 - The interest in fluid dynamics
12:00 - Caltech, Jerry Marsden, and the move to the Pacific time zone
19:43 - Dynamic Mode Decomposition (DMD) and the Koopman operator
27:15 - On teaching and the Eigensteve channel
39:22 - SINDy: Sparse Identification of Nonlinear Dynamics
45:45 - Automatic knowledge creation and Explainable AI
54:31 - HydroGym: RL benchmarks for fluid flow control
1:01:37 - Optimization boot camp
1:05:31 - Collimator
1:13:18 - Outro
Links
Steve's website: https://www.eigensteve.com/
Eigensteve channel: https://www.youtube.com/c/eigensteve
Jerrold E. Marsden: https://en.wikipedia.org/wiki/Jerrold_E._Marsden
Aphantasia: https://en.wikipedia.org/wiki/Aphantasia
J. Nathan Kutz: https://amath.washington.edu/people/j-nathan-kutz
Clarence W. Rowley: https://cwrowley.princeton.edu/
DMD: https://en.wikipedia.org/wiki/Dynamic_mode_decomposition
Koopman operator: https://en.wikipedia.org/wiki/Koopman_operator
Dynamic Mode Decomposition book: https://epubs.siam.org/doi/book/10.1137/1.9781611974508
On Dynamic Mode Decomposition paper: https://doi.org/10.3934/jcd.2014.1.391
DMD with control: https://arxiv.org/abs/1409.6358
Compressed sensing and DMD: https://doi.org/10.3934/jcd.2015002
Modern Koopman Theory for Dynamical Systems: https://arxiv.org/abs/2102.12086
Deep learning for universal linear embeddings of nonlinear dynamics: https://doi.org/10.1038/s41467-018-07210-0
Data-driven discovery of Koopman eigenfunctions for control: https://doi.org/10.1088/2632-2153/abf0f5
PyDMD: https://github.com/PyDMD
Discovering governing equations from data by sparse identification of nonlinear dynamical systems: https://doi.org/10.1073/pnas.1517384113
Data-driven discovery of partial differential equations:
https://doi.org/10.1126/sciadv.1602614
SINDy for model predictive control in the low-data limit:
https://doi.org/10.1098/rspa.2018.0335
PySINDy: https://github.com/dynamicslab/pysindy
SINDy with control: https://arxiv.org/abs/2108.13404
SINDy review: https://doi.org/10.1146/annurev-control-030123-015238
Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control: http://www.databookuw.com
Explainable AI: Learning from the Learners: https://arxiv.org/abs/2601.05525
HydroGym: https://github.com/dynamicslab/hydrogym