Interest in BOp-DMD?

[Michaelhess17]

Bagged, optimized DMD (BOp-DMD) is the most accurate DMD algorithm I am aware of due to its use of variable projection rather than direct time-stepping. This reduces or eliminates the bias in the derived eigenvalues. The bagged version of the method is both more accurate than individual fits and allows for estimation of error bars on predictions, as well. More about the algorithm can be found here: Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification.

I implemented a version in Julia based entirely on the bopdmd.py file from the PyDMD repository. My version of this code is here I am still in the process of optimizing performance and testing the code as much as possible, but if there is interest in integrating the port I have into the DataDrivenDiffEq.jl package, let me know and I can work on it! I would love to get all of the functionality of PyDMD into DataDrivenDiffEq.jl and possibly extend it more!

[ChrisRackauckas]

I'm super interesting. Indeed, that is what this repo is for! We just haven't been as active in this part of SciML but hey, if you're available it sounds like a good time to revive this effort a bit. I can help with the performance bits if you open the PR.

I would love to get all of the functionality of PyDMD into DataDrivenDiffEq.jl and possibly extend it more!

Yes, that is definitely a goal we have.

[Michaelhess17]

Awesome! I'll work on getting the initial PR started.

My use case is probably (?) not the expected scenario: I want to fit a lot of medium-sized models in parallel, both across datasets (trials) and within a trial with bagged indices. I'm pushing the limits of my CPU/RAM with threading currently (using large delay embedding dimensions), so I've considered parallelizing using CUDA.jl/KernelAbstractions.jl. I doubt that falls within the purview of SciML.jl though, so I'm happy to write everything for whatever the expectation is!

[ChrisRackauckas]

Reactant.jl has a lot of auto-distributed+GPU stuff going on, so the standard now would be to trace with Reactant and use that for the acceleration. We haven't adopted it everywhere yet and its docs are not fully complete, but there's unshared results that this distributes well to thousands of GPUs/TPUs, so we're already updating other libraries to it (NeuralOperators, NeuralPDE is next, ...) and this one is due for some Reactant-ification.