Model selection from a large ensemble of models
A method, system and processor readable medium containing computer readable software instructions for selecting representative models from a large ensemble of models is disclosed. An ensemble of reservoir models that define an input uncertainty space is provided. A target number of representative models and one or more target percentiles of output variables that the representative models are to approximate are input. The representative models from the ensemble of reservoir models that match the one or more target percentiles of output variables are selected while maximizing the spread between the selected representative models in the input uncertainty space.
1. A computer-implemented method for model selection, the computer-implemented method comprising:
(a) providing an ensemble of reservoir models for a reservoir that define an input uncertainty space;
(b) inputting a target number of representative models and one or more target percentiles of output variables that the representative models are to approximate;
(c) selecting the representative models from the ensemble of reservoir models that match the one or more target percentiles of output variables while maximizing the spread between the selected representative models in the input uncertainty space, wherein selecting the representative models from the ensemble of reservoir models comprises solving a single constrained minimax optimization problem, and wherein the single constrained minimax optimization problem is represented mathematically as:
for i = 1: nTrials
for j = 1: P
X
j
=
arg
rand
X
j
∈
C
{
(
max
k
min
l
y
k
j
-
y
_
k
l
y
_
k
l
)
<
ɛ
}
∀ k = 1, . . . , M: l = 1, . . . , P − j + 1
sub to:
∀ q = j − 1, . . . , 1
nnz(prctile(Y j ) == prctile(Y q )) = 0
end
end;
and
(d) modeling a behavior of the reservoir using the selected representative models.
2. The computer-implemented method of claim 1 , wherein the single constrained minimax optimization problem is solved directly by enumeration.
3. The computer-implemented method of claim 1 , wherein the single constrained minimax optimization problem is solved by Markov chain Monte Carlo methods.
4. The computer-implemented method of claim 1 , wherein the single constrained minimax optimization problem is solved using a greedy method with randomization.
5. The computer-implemented method of claim 1 , wherein the single constrained minimax optimization problem is solved using a global exhaustive search.
6. The computer-implemented method of claim 1 , further comprising selecting the representative models from the ensemble of reservoir models by solving two minimax optimization problems sequentially.
7. A system for model selection, the system comprising:
a database configured to store an ensemble of reservoir models for a reservoir that define an input uncertainty space;
a computer processor configured to receive the ensemble of reservoir models that define the input uncertainty space from the database, and to execute computer readable software instructions; and
a software program executable on the computer processor, the software program containing computer-readable software instructions to:
input a target number of representative models and one or more target percentiles of output variables that the representative models are to approximate; and
select the representative models from the ensemble of reservoir models that match the one or more target percentiles of output variables while maximizing the spread between the selected representative models in the input uncertainty space, wherein selecting the representative models from the ensemble of reservoir models comprises solving a single constrained minimax optimization problem, and wherein the single constrained minimax optimization problem is represented mathematically as:
for i = 1: nTrials
for j = 1: P
X
j
=
arg
rand
X
j
∈
C
{
(
max
k
min
l
y
k
j
-
y
_
k
l
y
_
k
l
)
<
ɛ
}
∀ k = 1, . . . , M: l = 1, . . . , P − j + 1
sub to:
∀ q = j − 1, . . . , 1
nnz(prctile(Y j ) == prctile(Y q )) = 0
end
end;
and
(d) model a behavior of the reservoir using the selected representative models.
8. The system of claim 7 , wherein the single constrained minimax optimization problem is solved directly by enumeration.
9. The system of claim 7 , wherein the single constrained minimax optimization problem is solved by Markov chain Monte Carlo methods.
10. The system of claim 7 , wherein the single constrained minimax optimization problem is solved using a greedy method with randomization.
11. The system of claim 7 , wherein the single constrained minimax optimization problem is solved using a global exhaustive search.
12. The system of claim 7 , wherein the software program further comprises computer-readable software instructions, that upon execution on the processor, select the representative models from the ensemble of reservoir models by solving two minimax optimization problems sequentially.
13. A non-transitory processor readable medium containing computer-readable software instructions for model selection, the computer-readable software instructions having instructions to:
obtain information from a database storing an ensemble of reservoir models for a reservoir that define an input uncertainty space;
input a target number of representative models and one or more target percentiles of output variables that the representative models are to approximate; and
select the representative models from the ensemble of reservoir models that match the one or more target percentiles of output variables while maximizing the spread between the selected representative models in the input uncertainty space, wherein selecting the representative models from the ensemble of reservoir models comprises solving a single constrained minimax optimization problem, and wherein the single constrained minimax optimization problem is represented mathematically as:
for i = 1: nTrials
for j = 1: P
X
j
=
arg
rand
X
j
∈
C
{
(
max
k
min
l
y
k
j
-
y
_
k
l
y
_
k
l
)
<
ɛ
}
∀ k = 1, . . . , M: l = 1, . . . , P − j + 1
sub to:
∀ q = j − 1, . . . , 1
nnz(prctile(Y j ) == prctile(Y q )) = 0
end
end;
and
(d) model a behavior of the reservoir using the selected representative models.
14. The non-transitory processor readable medium of claim 13 , wherein the single constrained minimax optimization problem is solved directly by enumeration.
15. The non-transitory processor readable medium of claim 13 , wherein the single constrained minimax optimization problem is solved by Markov chain Monte Carlo methods.
16. The non-transitory processor readable medium of claim 13 , wherein the single constrained minimax optimization problem is solved using a greedy method with randomization.
17. The non-transitory processor readable medium of claim 13 , wherein the single constrained minimax optimization problem is solved using a global exhaustive search.
18. The non-transitory processor readable medium of claim 13 , wherein the computer-readable software instructions further comprises instructions to select the representative models from the ensemble of reservoir models by solving two minimax optimization problems sequentially.