ModelOrderReduction.jl
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Operator Inference Model Order Reduction
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https://arxiv.org/abs/2205.02304 https://arxiv.org/abs/2102.00083
These are really all variations/extensions/relatives of DMD at the end of the day (lots of stuff related to DMD is already implemented in https://github.com/SciML/DataDrivenDiffEq.jl). So consider peaking there for inspiration.
One of the coolest papers I have read this year about this. Should definitely be considered: https://arxiv.org/abs/2112.04307
For references on DMD stuff : here's a python lib from Munich. :D https://datafold-dev.gitlab.io/datafold/references.html