缩放抛物面和导数检查

Question

我对 check_partial_derivatives() 方法应用于我上一个问题中显示的问题的输出感到惊讶：。当我添加对该方法的调用时：

from __future__ import print_function
import sys

from openmdao.api import IndepVarComp, Component, Problem, Group, ScipyOptimizer

class Paraboloid(Component):

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

        self.add_param('x', val=0.0)
        self.add_param('y', val=0.0)

        self.add_output('f_xy', val=0.0)

    def solve_nonlinear(self, params, unknowns, resids):

        x = params['x']
        y = params['y']

        #unknowns['f_xy'] = (x-3.0)**2 + x*y + (y+4.0)**2 - 3.0
        unknowns['f_xy'] = (1000.*x-3.)**2 + (1000.*x)*(0.01*y) + (0.01*y+4.)**2 - 3.

    def linearize(self, params, unknowns, resids):
        """ Jacobian for our paraboloid."""
        x = params['x']
        y = params['y']
        J = {}

        #J['f_xy', 'x'] = 2.0*x - 6.0 + y
        #J['f_xy', 'y'] = 2.0*y + 8.0 + x
        J['f_xy', 'x'] = 2000000.0*x - 6000.0 + 10.0*y
        J['f_xy', 'y'] = 0.0002*y + 0.08 + 10.0*x

        return J

if __name__ == "__main__":

    top = Problem()

    root = top.root = Group()
    #root.fd_options['force_fd'] = True

    root.add('p1', IndepVarComp('x', 3.0))
    root.add('p2', IndepVarComp('y', -4.0))
    root.add('p', Paraboloid())

    root.connect('p1.x', 'p.x')
    root.connect('p2.y', 'p.y')

    top.driver = ScipyOptimizer()
    top.driver.options['optimizer'] = 'SLSQP'

    top.driver.add_desvar('p1.x', lower=-1000, upper=1000, scaler=1000.)
    top.driver.add_desvar('p2.y', lower=-1000, upper=1000, scaler=0.001)
    top.driver.add_objective('p.f_xy')


    top.setup()
    top.check_partial_derivatives()  # added line
    top.run()


    print('\n')
    print('Minimum of %f found at (%f, %f)' % (top['p.f_xy'], top['p.x'], top['p.y']))

我得到以下输出：

Partial Derivatives Check

----------------
Component: 'p'
----------------
  p: 'f_xy' wrt 'x'

    Forward Magnitude : 6.000000e+03
    Reverse Magnitude : 6.000000e+03
         Fd Magnitude : 2.199400e+07

    Absolute Error (Jfor - Jfd) : 2.200000e+07
    Absolute Error (Jrev - Jfd) : 2.200000e+07
    Absolute Error (Jfor - Jrev): 0.000000e+00

    Relative Error (Jfor - Jfd) : 1.000273e+00
    Relative Error (Jrev - Jfd) : 1.000273e+00
    Relative Error (Jfor - Jrev): 0.000000e+00

    Raw Forward Derivative (Jfor)

[[-6000.]]

    Raw Reverse Derivative (Jrev)

[[-6000.]]

    Raw FD Derivative (Jfor)

[[ 21994001.]]
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  p: 'f_xy' wrt 'y'

    Forward Magnitude : 8.000000e-02
    Reverse Magnitude : 8.000000e-02
         Fd Magnitude : 2.200000e+07

    Absolute Error (Jfor - Jfd) : 2.200000e+07
    Absolute Error (Jrev - Jfd) : 2.200000e+07
    Absolute Error (Jfor - Jrev): 0.000000e+00

    Relative Error (Jfor - Jfd) : 1.000000e+00
    Relative Error (Jrev - Jfd) : 1.000000e+00
    Relative Error (Jfor - Jrev): 0.000000e+00

    Raw Forward Derivative (Jfor)

[[ 0.08]]

    Raw Reverse Derivative (Jrev)

[[ 0.08]]

    Raw FD Derivative (Jfor)

[[ 22000000.08]]
Optimization terminated successfully.    (Exit mode 0)
            Current function value: [-27.33333333]
            Iterations: 4
            Function evaluations: 6
            Gradient evaluations: 4
Optimization Complete
-----------------------------------


Minimum of -27.333333 found at (0.006667, -733.333333)

优化是正确的（即几乎可以肯定地证明导数是正确的），但是 check_partial_derivatives 输出没有显示 fd 和 forward/reverse 方法之间一致的结果。

Answer 1

参考

因此，您遇到了之前出现的限制，即您无法计算关于设计点的导数，直到您运行您的模型在那个点。有限差分结果是错误的，因为模型从来没有运行。要验证您的部分，您需要将 check_partial_derivatives 移动到运行之后。此外，我总是在检查导数时注释掉优化器，以便检查关于初始点的导数。当我做这两件事时，我得到了很好的结果（见下面的代码）。

top = Problem()

root = top.root = Group()
#root.fd_options['force_fd'] = True

root.add('p1', IndepVarComp('x', 3.0))
root.add('p2', IndepVarComp('y', -4.0))
root.add('p', Paraboloid())

root.connect('p1.x', 'p.x')
root.connect('p2.y', 'p.y')

#top.driver = ScipyOptimizer()
#top.driver.options['optimizer'] = 'SLSQP'

#top.driver.add_desvar('p1.x', lower=-1000, upper=1000, scaler=1000.)
#top.driver.add_desvar('p2.y', lower=-1000, upper=1000, scaler=0.001)
#top.driver.add_objective('p.f_xy')

top.setup()
top.run()
top.check_partial_derivatives()  # added line

print('\n')
print('Minimum of %f found at (%f, %f)' % (top['p.f_xy'], top['p.x'], top['p.y']))

我们的 github 上有一项功能请求，要求能够运行 check_partial_derivatives 无需先运行模型。我认为我们可以通过只告诉 root solve_nonlinear，忽略驱动程序来做到这一点，所以它可能会在某个时候添加。

缩放抛物面和导数检查

Scaled paraboloid and derivatives checking

python

openmdao