[Numpy-discussion] Interpolation question

[Andrea Gavana]

(Resending as numpy-discussion has a 40 Kb message limit)

On 30 March 2010 22:44, Friedrich Romstedt <friedrichromstedt at gmail.com> wrote:
> 2010/3/30 Andrea Gavana <andrea.gavana at gmail.com>:
>> However, from the first 100 or so interpolated simulations, I could
>> gather these findings:
>>
>> 1) Interpolations on *cumulative* productions on oil and gas are
>> extremely good, with a maximum range of relative error of -3% / +2%:
>> most of them (95% more or less) show errors < 1%, but for few of them
>> I get the aforementioned range of errors in the interpolations;
>> 2) Interpolations on oil and gas *rates* (time dependent), I usually
>> get a -5% / +3% error per timestep, which is very good for my
>> purposes. I still need to check these values but the first set of
>> results were very promising;
>> 3) Interpolations on gas injection (cumulative and rate) are a bit
>> more shaky (15% error more or less), but this is essentially due to a
>> particular complex behaviour of the reservoir simulator when it needs
>> to decide (based on user input) if the gas is going to be re-injected,
>> sold, used as excess gas and a few more; I am not that worried about
>> this issue for the moment.
>
> Have a nice time in Greece, and what you write makes me laughing. :-)
> When you are back, you should maybe elaborate a bit on what gas
> injections, wells, re-injected gas and so on is, I don't know about
> it.

Just as a little follow-up, I managed to obtain a more extended set of
interpolated simulations yesterday. As a little recap, I took two
thirds of the simulations database to use them as interpolation base
and tried to reproduce the rest using the interpolation. I have a
couple of plots to demonstrate how good/bad the interpolation was.

1) The first one (http://img404.yfrog.com/img404/9885/doterrors.png)
has 6 subplots: the first 3 at the
top show relative errors (in percentage) for cumulative productions
for oil and gas and cumulative gas injection, with:

relative_error = 100 * (real - interpolated) / real

The second set of 3 subplots at the bottom show median errors on
oil/gas production rates and gas injection rates: these are series of
time-dependent values (in contrast to the cumulative, which are a
single floating point value), so I took the median error over all the
simulated timesteps.

As you can see, about 95-96% of the interpolated results have a
relative error between -5% / +5%, with some outliers (which don't
bother me that much anyway :-D ).

2) The second figure
(http://img338.imageshack.us/img338/7527/boxploterrors.png) has been
liberally adapted
from a matplotlib demo (boxplot_demo2), and show a series of error box
plots for all the variables I have used in the interpolation.

Overall, I can say I am pretty satisfied with the results :-D . If I
get a chance to test Kevin's and Robert's ideas before getting sent to
Kazakhstan I'll post another follow-up, unless you got bored by now
and you tell me to shut up.

Thank you again to the list for the wonderful help.

Andrea.

"Imagination Is The Only Weapon In The War Against Reality."
http://xoomer.alice.it/infinity77/

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