Notes and next steps from meeting on 10/26/2021 with Khachik

[saeed-moghimi-noaa]

Saeed notes from meeting on 10/26/2021 with Khachik

@WPringle and @zacharyburnettNOAA see if this note is useful.

Notes for William

• using a polynomial for the surrogate might not be the best method for maximum elevations
  • because it might be “jumpy” (discontinuous) - perhaps look into time series for PC?
  • 3rd order polynomial might be overfitting because of too many degrees of freedom
    surrogate
  • if we can’t use polynomials, we will have to move to a more flexible scheme
    • neural network (don’t get sensitivities for free)
• plot map of sensitivities using function provided in document
• To figure out to do percentile !?
  • in high-dimensional (more than 4) random variables, "there is no such thing as quantile"

Notes for Zach

• quadrature can be more accurate with less samples, but could fail for discontinued parameters
• take out the original run from the quadrature fit - otherwise the quadrature will break
• repeat the same sample with regression
• try KL or PCA

Notes for Both

• try validating the surrogate with 50 or so reference samples separate from the training set
  • plot the fit against the training data
  • if the training set fits well but validation set does NOT fit well, then the surrogate model is overfit
• use Equation 6 from doc to go from math space to physical space - "everything should go through Equation 6"
• try testing a single mesh node
  • pick a single node
  • gather maximum elevations
  • build surrogate
  • compare percentiles

Things we can Try

• perhaps we can ravel time into the node space
  • compress time axis with KL eigenvalues
  • either way we will have to sparsify nodes
• perhaps we can decompose the matrix
  • what we need is the covariance of the entire matrix
  • aggregate with dask?
• sparsify time series
  • get 12 hour leadup time to storm landfall
  • every 2 hours

[saeed-moghimi-noaa]

Fold time, lat and lon and pass it to KL or PCA to compress it. Perhaps instead of 5 or 6 mode we may get 10s of modes.

• go every m spatial point and every n time point
• use MPI or some sort of parallel implementation

[WPringle]

https://ml.dask.org/modules/generated/dask_ml.decomposition.PCA.html