how to surrogate model with multiple variable?

[nguyenhoaiThanhbk2811]

I have the three parameters (node1,node2,node2) with each parameters I have 20 values. nodes1 = np.array([0.05675, 0.05934, 0.05633, 0.0557 , 0.05702, 0.06401, 0.06322, 0.06571, 0.06099, 0.05832, 0.06196, 0.06463, 0.05507, 0.06351, 0.06287, 0.06122, 0.05407, 0.05985, 0.05774,0.06015])

nodes2 = np.array([0.9486, 0.9095, 0.9856, 0.9318, 1.0477, 1.0489,1.0663, 0.9184, 0.9646, 1.0345, 1.0168, 1.0565, 0.9727, 0.9907, 0.9277, 0.9548, 1.0933, 1.0751,1.0026, 1.0231])

nodes3 = np.array([51.813, 54.279, 52.659, 51.197 , 46.629, 49.791, 48.581, 54.799, 46.413, 47.078, 52.367, 48.204, 50.389, 45.402, 47.893, 50.796 , 49.332, 53.323, 53.713, 45.757])

with a group parameter of input I have a output values. So I have the 20 output values example: (node1_1,node2_1,node3_1)=(0.05675,0.9486,51.813) I have a output values = 0.0204232

output=np.array([0.0204232,0.0205054,0.0204971,0.0204463,0.0206686,0.0206678,0.0206883,0.0204627,0.020426,0.0206532,0.0206322,0.020677,0.0204431,0.0205319,0.0204508,0.0204115,0.020721,0.0206988,0.0206179,0.0206418])

How to estimate the surrogate model between (node1,node2,node3) with output? and how to know the detail equation of the surrogate model?

please help me, thanks you

[dme65]

Your data points should have size 20 x 3 since you have 20 points in 3 dimensions.

A simple example where you build a cubic RBF from 100 data points in 3 dimensions may look like this:

import numpy as np
from pySOT.surrogate import RBFInterpolant, CubicKernel, LinearTail

np.random.seed(0)
X = np.random.rand(100, 3)
y = np.sin(np.sum(X, 1))
rbf = RBFInterpolant(dim=3, kernel=CubicKernel(), tail=LinearTail(dim=3), eta=1e-6)
rbf.add_points(X, y)
print(rbf.predict(np.zeros((1, 3))))  # Should be close to 0

Output:

[[0.01681138]]

The functional form of the surrogate model depends on what model you're using. RBFs aren't easily interpretable from the model weights, but other models like polynomial regression are.

[Zosezhuo]

Hello,

My query is related to the above example.

Using your example above, I would like to build a cubic RBF over 20 points in 3*3 dimensions.

Does pySOT support this feature?

Thank you!

[dme65]

Hi Zosezhuo, Can you clarify what you mean by 3*3 dimensions?

[Zosezhuo]

Hi

Specifically, I would like to do the following in 3 by 3 dimensions.

np.random.seed(0)
X = np.random.uniform(low=0.0, high=1.0, size=[3,3])
y= fun(X)
y2= fun2(X)

print(X)
print(y)
print(y2)

[[0.5488135  0.71518937 0.60276338]
 [0.54488318 0.4236548  0.64589411]
 [0.43758721 0.891773   0.96366276]]
134408.75071136828
3.144276104044118

When I tried to add points, I received the following output

rbf_cubic = RBFInterpolant(dim=[3,3], kernel=CubicKernel(), tail=LinearTail(dim=[3,3]), eta=1e-6)
rbf_cubic.add_points(X, y)
rbf_cubic.add_points(X, y2)

TypeError: unsupported operand type(s) for +: 'int' and 'list

Appreciate your time and help very much

[dme65]

An RBF interpolant is a function from R^d -> R. You need to pass in a matrix X with shape (n, d) and y with shape (n,).