Open odunbar opened 1 year ago
Note on timestepping in momentum-accelerated EKP methods: Our goal is to implement momentum-inspired accelerators without changing existing update methods, as detailed above. EKI and "momentum-accelerated" EKI apply virtually the same update, but scale by dt and dt^2 respectively. It is possible that this distinction won't cause a problem in individual applications, since we have optimized timesteppers in place. That said I will need to verify that the currently-implemented EKP timestep (related to the observation error covariance) makes sense in the accelerated context.
Offline we have been experimenting with a few momentum-based accelerations of EKI with good success. Integration of such approaches into the code for application with general EKP-type methods is detailed below. In general we have identified a rough template of what such accelerators will look like:
It is also important that the saved pairs are the momentum-shifted ensemble members and the evaluations of them (i.e.
v
andG(v)
remain consistent). This works because accelerators typically still involve the calculation of a typical gradient-based update, and are simply followed by a perturbation of the particles by momentum.Hopefully UKI,EKI,Transform-EKI,SEKI, (maybe even EKS, which also represents a gradient flow) can be all be updated with the same interface.
Happy to iterate a bit here.