Question

我尝试使用OpenMDAO解决简单的隐式方程。方程式如下所示，
x * z + z - 4 = 0
y = x + 2 * z

对于x = 0.5，解是z = 2.666667，y = 5.833333。

对于这种情况，我使用了下面显示的代码，

from __future__ import print_function

from openmdao.api import Component, Group, Problem, Newton, ScipyGMRES

class SimpleEquationSystem(Component):
    """Solve the Equation 
            x*z + z - 4 = 0
            y = x + 2*z

       Solution: z = 2.666667, y = 5.833333 for x = 0.5
    """

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


        self.add_param('x', 0.5)
        self.add_state('y', 0.0)
        self.add_state('z', 0.0)
        self.iter=0

    def solve_nonlinear(self, params, unknowns, resids):
        """This component does no calculation on its own. It mainly holds the
        initial value of the state. An OpenMDAO solver outside of this
        component varies it to drive the residual to zero."""
        pass

    def apply_nonlinear(self, params, unknowns, resids):
        """ Report the residual """
        self.iter+=1
        x=params['x']
        y = unknowns['y']
        z = unknowns['z']


        resids['y'] = x*z + z - 4
        resids['z'] = x + 2*z - y

        print('y_%d' % self.iter,'=%f' %resids['y'], 'z_%d' % self.iter, '=%f' %resids['z'])
        print('x' ,'=%f' %x, 'y', '=%f' %y, 'z', '=%f' %z)

top = Problem()
root = top.root = Group()
root.add('comp', SimpleEquationSystem())


# Tell these components to finite difference
root.comp.deriv_options['type'] = 'fd'
root.comp.deriv_options['form'] = 'central'
root.comp.deriv_options['step_size'] = 1.0e-4
root.nl_solver = Newton()
root.ln_solver = ScipyGMRES()

top.setup()
top.print_all_convergence(level=1, depth=2)
top.run()
print('Solution x=%.2f, y=%.2f, z=%.2f' % (top['comp.x'], top['comp.y'], top['comp.z']))

我根据Solving an Implicit Relationship with a Newton Solver方法编写了一个代码。要运行此代码，我得到了这样的解决方案，

##############################################
Setup: Checking root problem for potential issues...

No recorders have been specified, so no data will be saved.

The following parameters have no associated unknowns:
comp.x

The following components have no connections:
comp

Setup: Check of root problem complete.
##############################################

y_1 =-4.000000 z_1 =0.500000
x =0.500000 y =0.000000 z =0.000000
y_2 =-4.000000 z_2 =0.499900
x =0.500000 y =0.000100 z =0.000000
y_3 =-4.000000 z_3 =0.500100
x =0.500000 y =-0.000100 z =0.000000
y_4 =-3.999850 z_4 =0.500200
x =0.500000 y =0.000000 z =0.000100
y_5 =-4.000150 z_5 =0.499800
x =0.500000 y =0.000000 z =-0.000100
   [root] LN: GMRES   1 | 0 0
   [root] LN: GMRES   1 | Converged in 1 iterations
y_6 =-inf z_6 =-inf
x =0.500000 y =inf z =-inf
y_7 =-inf z_7 =-inf
x =0.500000 y =inf z =-inf
y_8 =-inf z_8 =-inf
x =0.500000 y =inf z =-inf
y_9 =-inf z_9 =-inf
x =0.500000 y =inf z =-inf
y_10 =-inf z_10 =-inf
x =0.500000 y =inf z =-inf
   [root] LN: GMRES   1000 | nan nan
   [root] LN: GMRES   1000 | Converged in 1000 iterations
y_11 =nan z_11 =nan
x =0.500000 y =nan z =nan
[root] NL: NEWTON   2 | nan nan (nan)
[root] NL: NEWTON   2 | FAILED to converge after 2 iterations
Solution x=0.50, y=nan, z=nan
C:\ProgramData\Anaconda3\Anaconda3\lib\site-packages\openmdao\core\system.py:750: RuntimeWarning: invalid value encountered in subtract
  resultvec.vec[:] -= cache2

你能知道，如何用各自的迭代解决这个问题？并告诉我，如何构建solve_nonlinear＆amp;适用于这种情况的apply_nonlinear。

Answer 1

当您为自变量添加Indepvarcomp时，看起来问题会清除：

root.add('p1', IndepVarComp('x', 0.5))
root.add('comp', SimpleEquationSystem())
root.connect('p1.x', 'comp.x')

然后它迅速收敛。

[root] NL: NEWTON   1 | 2.73692411e-11 6.7894731e-12 (6.41396046825)
[root] NL: NEWTON   1 | Converged in 1 iterations

我同意你不应该为此添加它，这可能是一个错误。我已经确认在我们最新的OpenMDAO开发版本中已修复此问题。

如何解决OpenMDAO中的方程系统？

1 个答案: