Folding Data

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G

gabelucas

Guest
I frequently see references to folding a model over data, such as "folding a full phase model like RGBM over profiles" (-BRW).

What does this term mean? What is involved in folding a model over data? Is it tweeking an algorithm to fit real-world experience?

-=[Gabe]=-
 
Gabe,

Yes.

Folding data for RGBM means taking some 1700+ real
dives and fine tuning 14 model dependent parameters
by maxiumum likelihood to this data.

The error norm in fits is L2 (differences squared) and
this is minimized in 14 parameter space over the whole
profile.

See TDID, RGBM In Depth, or Basic Deco Theory And
Apps.

Regards,

Bruce Wienke
Program Manager Computational Physics
C & C Dive Team Ldr
 
Dear gabe:

“Folding”

I guess I know this as “parameterization.” Almost all models incorporate data to adjust some parameters (constants). It is generally thought that the fewer the number of adjustable parameters, the better the model. With biological systems, the number of needed parameters generally is several.

It is often said that, if you have enough adjustable parameters, anything can be suitably fitted to a model. In some models, the parameters have definite, assignable values. These parameters could be:

surface tension, temperature, viscosity, initial nucleus radius, micronuclei size-number distribution, modulus of tissue elasticity, solubility of gas in water, solubility of gas lipid, diffusivity [in several possible places], blood flow rate, surfactant concentration, etc.


There are methods to match, or fit, multiple constants in an equation to data sets. Without a computer to do the calculations, anything but the simplest is not really possible. However, if the computer is large enough and/or you are willing to have the machine invest the time, you can adjust the model parameters (constants) to give the best fit. If the constants/parameters are realistic, then you know that the model might be correct to a major degree. If the “model fits” are not really what you expected, then probably the computer is forcing the constants to fit the data. You will get numbers that are “spooky.” For example, you might get a surface tension that is 15 dynes/cm when you expect it to be somewhere are 60 dynes/cm. Or you might get a diffusion constant that is 10 [exp] –10 rather than what might be expected, viz, 10 [exp] – 5.

The agreement of a model to reality is not a definite proof of its veracity. The Haldane model worked quite well within a certain range, however, the idea of critical supersaturation limits was incorrect.

Dr Deco :doctor:
 
All,

RGBM is both realistic and parameter space matches
reality in constants, whether fixed, fitted, or tuned.

Note I said "tuning", NOT "fitted because we have no idea".

In RGBM, all constants are SET (as you can see in RGBM
In Depth). The 1700+ dive profiles can backstrap RGBM
and allow further "subfitting" to models which do not
do full RGBM and phase mechanics.

Plus more.

The 1700+ profiles also serve as a reality tune on
already set constants, for internal self-consistency.
As RGBM Data Bank grows, so will profile size, finer
tuning, etc.

Constants/inputs in RGBM calcs include:

previous dives (input)

altitude (input)

temperature (input)

lipid or aqueous EOS for bubble skins (fixed on input)

surfactant material strength (EOS plus temp and pressure)

diffusion length for gas transfer (EOS plus temp and pressure)

surface tension (EOS plus temp and pressure)

tissue halftimes (input)

Boyle response (EOS plus temp plus pressure)

He and N2 solubility (temp and pressure)

mass transport coefficients (diffusivity times solubility)

separated phase volume limit (fixed for mix)

micronuclei number distribution (fixed for mix and temp)

micronuclei regeneration time (fixed for mix and temp)

excitation radius (fixed for distribution, pressure, and temp)

viscosity and elasticity (fixed by EOS)

To see how these go together, and other info on testing
and validation, check out the refs I have been spouting
the past few weeks or so.

Regards,

Bruce Wienke
Program Manager Computational Physics
C & C Dive Team Ldr
 

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