automatic parametric space exploration and boundary detection.
Hi all,
I am not sure where to ask about my "strange" question, so as an initial
attempt, I post it here.
I have a parameterized function f(x, y, z, u, v), which takes values on
{0,
1}, i.e. either 0 or 1.
Through experimenting I've found that when plotting out in 2D there is a
clear linear cut in the parameter space.
If I plot f(1, y, z, 5, 7) as a mesh of grid size 0.1, the cut is a
straight
line, the region below this line has f=1, and the region above this line
has
f=0.
If I plot f(2, y, z, 5, 7) as a mesh of grid size 0.1, the cut is a
straight
line, the region below this line has f=1, and the region above this line
has
f=0. The only difference is that this line ****fted.
....
If I plot f(x, 1, z, 5, 7) and f(x, 2, z, 5, 7) etc., still there is a
linear cut splitting the space.
....
If I plot f(x, y, 1, 5, 7) and f(x, y, 2, 5, 7) etc., still there is a
linear cut splitting the space.
....
It looks like there is a space-cutting plane in my parameter space.
But the grid size is 0.1, I still have a hard time figuring out what will
happen when grid size becomes 0.01 and 0.001, etc.
But still, I would like to discover how to define this cutting plane
mathematically... ba
My function is too complicated, and can only be computed numerically, so I
had a hard time finding a closed form for this cutting plane.
Is there a way to determine the cutting plane using some automatifc
procedure?
I mean, it looks like some kind of optimization procedure, it seeks the
finest boundry in the space such that on the left of the cut, f=1 and on
the
other side of the cut, f=0. It also looks like a regression problem. But
so
far I am still not sure how to model it.
Can anybody give me some suggestions and comments?
Thanks a lot!
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