[Numpy-discussion] Interpolation question

Brennan Williams brennan.williams@visualreservoir....
Mon Mar 29 17:13:42 CDT 2010


Andrea Gavana wrote:
> Hi Chris and All,
>
> On 29 March 2010 22:35, Christopher Barker wrote:
>   
>> Andrea Gavana wrote:
>>     
>>>>> Scaling each axis by its standard deviation is a typical first start.
>>>>> Shifting and scaling the values such that they each go from 0 to 1 is
>>>>> another useful thing to try.
>>>>>           
>>>> Ah, magnifico! Thank you Robert and Friedrich, it seems to be working
>>>> now...
>>>>         
>> One other thought -- core to much engineering is dimensional analysis --
>> you know how we like those non-dimensional number!
>>
>> I think this situation is less critical, as you are interpolating, not
>> optimizing or something, but many interpolation methods are built on the
>> idea of some data points being closer than others to your point of interest.
>>
>> Who is to say if a point that is 2 hours away is closer or father than
>> one 2 meters away? This is essentially what you are doing.
>>
>> Scaling everything to the same range is a start, but then you've still
>> given them an implicit weighting.
>>
>> An alternative to to figure out a way to non-dimensionalize your
>> parameters -- that *may* give you a more physically based scaling.
>>
>> And you might invent the "Gavana Number" in the process ;-)
>>     
>
> Might be :-D . At the moment I am pretty content with what I have got,
> it seems to be working fairly well although I didn't examine all the
> possible cases and it is very likely that my little tool will break
> disastrously for some combinations of parameters. However, I am not
> sure I am allowed to post an image comparing the "real" simulation
> with the prediction of the interpolated proxy model, but if you could
> see it, you would surely agree that it is a very reasonable approach.
> It seems to good to be true :-D .
>
> Again, this is mainly due to the fact that we have a very extensive
> set of simulations which cover a wide range of combinations of
> parameters, so the interpolation itself is only doing its job
> correctly. I don't think the technique can be applied blindly to
> whatever oil/gas/condensate /whatever reservoir, as non-linearities in
> fluid flow simulations appear where you least expect them, but it
> seems to be working ok (up to now) for our field (which is, by the
> way, one of the most complex and less understood condensate reservoir
> out there).
>
>   
And of course that proxy simulator only deals with the input variables 
that you decided on 1,000+ simulations ago.
All you need is for someone to suggest something else like "how about 
gas injection?" and you're back to having to do
more real simulation runs (which is where a good experimental design 
comes in).

It would be interesting to know how well your proxy simulator compares 
to the real simulator for a combination of input variable values that
is a good distance outside your original parameter space.

Brennan

> Andrea.
>
> "Imagination Is The Only Weapon In The War Against Reality."
> http://xoomer.alice.it/infinity77/
>
> ==> Never *EVER* use RemovalGroup for your house removal. You'll
> regret it forever.
> http://thedoomedcity.blogspot.com/2010/03/removal-group-nightmare.html <==
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