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mathematicalmichael / mud-examples

Creation of figures for papers pertaining to the MUD (Maximal Updated Density) method for Parameter Estimation.
https://mud-examples.readthedocs.io/
MIT License
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use SVD to craft QoI #51

Closed mathematicalmichael closed 2 years ago

mathematicalmichael commented 2 years ago

sd = 0.05 with 500 measurements and 1000 samples. purple = mud from qoi created by split in the middle blue = use SVD on scaled residuals to discover weighting for definition of new QoI

image image 
num_qoi = 2
new_qoi_map = singular_vectors[0:num_qoi, :]
new_qoi = residuals @ new_qoi_map.T  # ok shape, wrong solution, identical to using U@sigma
image

however the colorbars there differ, as we can see by looking at the absolute values instead of the relative ones that result from the color-scaling per axis:

image

this indicates that the first QoI is more or less a mean-value of the sensors (weighing some samples more than others, but overall with very low variation), and the second QoI is incorporating information from the top/bottom halves, lining up nicely with our intuition about splitting the domain into horizontal slices.

If we look at our QoI response surfaces, we can see that we now have a map with orthogonal contours (in the eyeball norm)...

image
codecov-commenter commented 2 years ago

Codecov Report

Merging #51 (8d1d287) into main (1580c30) will increase coverage by 0.01%. The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main      #51      +/-   ##
==========================================
+ Coverage   77.92%   77.93%   +0.01%     
==========================================
  Files          14       14              
  Lines        1803     1804       +1     
  Branches      237      237              
==========================================
+ Hits         1405     1406       +1     
  Misses        313      313              
  Partials       85       85
Impacted Files Coverage Δ
src/mud_examples/poisson.py 84.75% <ø> (ø)
src/mud_examples/pde.py 73.38% <100.00%> (+0.21%) :arrow_up:

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