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SciML / ModelOrderReduction.jl

High-level model-order reduction to automate the acceleration of large-scale simulations
https://docs.sciml.ai/ModelOrderReduction/
MIT License
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Diffusion Map #17

Open dynamic-queries opened 2 years ago

dynamic-queries commented 2 years ago

For non-linear data reduction, Diffusion maps should be considered, as there is good deal of work done here wrt Data Driven MOR methods.

https://www.sciencedirect.com/science/article/pii/S1063520306000546?via%3Dihub

Implementation friendly description at https://mediatum.ub.tum.de/download/1356533/1356533.pdf , page 46

dynamic-queries commented 2 years ago

Could leverage implementations from https://github.com/wildart/ManifoldLearning.jl here. Although I would like to build on it for optimal embedding as they discuss here https://www.sciencedirect.com/science/article/pii/S1063520315000949?ref=cra_js_challenge&fr=RR-1 . @ChrisRackauckas Would it make sense re-implementing the diffusion maps to add this "optimal embedding feature" ?

ChrisRackauckas commented 2 years ago

Reusing code is usually good, though I know there are some issues with many of the diffusion map libraries in Julia so 🤷 . https://github.com/wildart/ManifoldLearning.jl has had maintenance issues since forever so reimplementing might be a fine idea.