Openmdao中克里格函数的梯度答案

【问题标题】：Gradient of kriged function in OpenmdaoOpenmdao中克里格函数的梯度
【发布时间】：2016-01-21 03:32:00
【问题描述】：

我目前正在编写多梯度下降算法，其中我使用克里格函数。我的问题是我找不到如何获得克里格函数的梯度（我尝试使用线性化但我不知道如何使它工作）。

    from __future__ import print_function

from six import moves
from random import shuffle
import sys
import numpy as np
from numpy import linalg as LA
import math
from openmdao.braninkm import F, G, DF, DG

from openmdao.api import Group, Component,IndepVarComp
from openmdao.api import MetaModel
from openmdao.api import KrigingSurrogate, FloatKrigingSurrogate

def rand_lhc(b, k):
    # Calculates a random Latin hypercube set of n points in k dimensions within [0,n-1]^k hypercube.
    arr = np.zeros((2*b, k))
    row = list(moves.xrange(-b, b))
    for i in moves.xrange(k):
        shuffle(row)
        arr[:, i] = row
    return arr/b*1.2


class TrigMM(Group):
    ''' FloatKriging gives responses as floats '''

    def __init__(self):
        super(TrigMM, self).__init__()

        # Create meta_model for f_x as the response
        F_mm = self.add("F_mm", MetaModel())
        F_mm.add_param('X', val=np.array([0., 0.]))
        F_mm.add_output('f_x:float', val=0., surrogate=FloatKrigingSurrogate())
       # F_mm.add_output('df_x:float', val=0., surrogate=KrigingSurrogate().linearize)


        #F_mm.linearize('X', 'f_x:float')
        #F_mm.add_output('g_x:float', val=0., surrogate=FloatKrigingSurrogate())
        print('init ok')
        self.add('p1', IndepVarComp('X', val=np.array([0., 0.])))
        self.connect('p1.X','F_mm.X')       

        # Create meta_model for f_x as the response
        G_mm = self.add("G_mm", MetaModel())
        G_mm.add_param('X', val=np.array([0., 0.]))
        G_mm.add_output('g_x:float', val=0., surrogate=FloatKrigingSurrogate())
        #G_mm.add_output('df_x:float', val=0., surrogate=KrigingSurrogate().linearize)

        #G_mm.linearize('X', 'g_x:float')
        self.add('p2', IndepVarComp('X', val=np.array([0., 0.])))
        self.connect('p2.X','G_mm.X')                 

from openmdao.api import Problem

prob = Problem()
prob.root = TrigMM()
prob.setup()

u=4 
v=3 

#training avec latin hypercube

prob['F_mm.train:X'] = rand_lhc(20,2)
prob['G_mm.train:X'] = rand_lhc(20,2)

#prob['F_mm.train:X'] = rand_lhc(10,2)
#prob['G_mm.train:X'] = rand_lhc(10,2)
#prob['F_mm.linearize:X'] = rand_lhc(10,2)
#prob['G_mm.linearize:X'] = rand_lhc(10,2)
datF=[]
datG=[]
datDF=[]
datDG=[]

for i in range(len(prob['F_mm.train:X'])):
    datF.append(F(np.array([prob['F_mm.train:X'][i]]),u))
    #datG.append(G(np.array([prob['F_mm.train:X'][i]]),v))
data_trainF=np.fromiter(datF,np.float) 

for i in range(len(prob['G_mm.train:X'])):
    datG.append(G(np.array([prob['G_mm.train:X'][i]]),v))   
data_trainG=np.fromiter(datG,np.float) 

prob['F_mm.train:f_x:float'] = data_trainF
#prob['F_mm.train:g_x:float'] = data_trainG
prob['G_mm.train:g_x:float'] = data_trainG

【问题讨论】：

标签： gradient kriging openmdao

【解决方案1】：

您要编写多梯度下降驱动程序吗？如果是这样，则 OpenMDAO 使用calc_gradient 方法计算从参数到Problem 级别的输出的梯度。

如果您查看 pyoptsparse 驱动程序的源代码：

https://github.com/OpenMDAO/OpenMDAO/blob/master/openmdao/drivers/pyoptsparse_driver.py

_gradfunc 方法是一个回调函数，它返回相对于设计变量的约束和目标的梯度。 Metamodel 组件为我们的所有（我认为）代理具有内置的分析梯度，因此您甚至不必在那里声明任何。

如果这不是您想要做的，那么我可能需要更多关于您的应用程序的信息。

【讨论】：