ModelOrderReduction.jl
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Balanced POD
This could be an extension to #2
Both are quite simple mathematically.
Original balanced POD method: https://arc.aiaa.org/doi/abs/10.2514/2.1570
Slight improvement of the original method: https://www.sciencedirect.com/science/article/pii/S0021999112002045
Very concise and approachable description (and improves Wilcox and Peraire's work from an algorithmic standpoint!) https://www.worldscientific.com/doi/abs/10.1142/S0218127405012429