OpenMDAO cache_linear_solution 未更新初始猜测

Question

我想通过使用以前的线性解作为优化中后续迭代的初始猜测来节省我优化的昂贵线性求解的时间。我正在查看 OpenMDAO 的 cache_linear_solution 功能示例，该功能似乎是为此目的而开发的（here），代码如下所示：

from distutils.version import LooseVersion
import numpy as np
import scipy
from scipy.sparse.linalg import gmres

import openmdao.api as om


class QuadraticComp(om.ImplicitComponent):
    """
    A Simple Implicit Component representing a Quadratic Equation.

    R(a, b, c, x) = ax^2 + bx + c

    Solution via Quadratic Formula:
    x = (-b + sqrt(b^2 - 4ac)) / 2a
    """

    def setup(self):
        self.add_input('a', val=1.)
        self.add_input('b', val=1.)
        self.add_input('c', val=1.)
        self.add_output('states', val=[0,0])

        self.declare_partials(of='*', wrt='*')

    def apply_nonlinear(self, inputs, outputs, residuals):
        a = inputs['a']
        b = inputs['b']
        c = inputs['c']
        x = outputs['states'][0]
        y = outputs['states'][1]

        residuals['states'][0] = a * x ** 2 + b * x + c
        residuals['states'][1] = a * y + b

    def solve_nonlinear(self, inputs, outputs):
        a = inputs['a']
        b = inputs['b']
        c = inputs['c']
        outputs['states'][0] = (-b + (b ** 2 - 4 * a * c) ** 0.5) / (2 * a)
        outputs['states'][1] = -b/a

    def linearize(self, inputs, outputs, partials):
        a = inputs['a'][0]
        b = inputs['b'][0]
        c = inputs['c'][0]
        x = outputs['states'][0]
        y = outputs['states'][1]

        partials['states', 'a'] = [[x**2],[y]]
        partials['states', 'b'] = [[x],[1]]
        partials['states', 'c'] = [[1.0],[0]]
        partials['states', 'states'] = [[2*a*x+b, 0],[0, a]]

        self.state_jac = np.array([[2*a*x+b, 0],[0, a]])

    def solve_linear(self, d_outputs, d_residuals, mode):

        if mode == 'fwd':
            print("incoming initial guess", d_outputs['states'])
            if LooseVersion(scipy.__version__) < LooseVersion("1.1"):
                d_outputs['states'] = gmres(self.state_jac, d_residuals['states'], x0=d_outputs['states'])[0]
            else:
                d_outputs['states'] = gmres(self.state_jac, d_residuals['states'], x0=d_outputs['states'], atol='legacy')[0]
        elif mode == 'rev':
            if LooseVersion(scipy.__version__) < LooseVersion("1.1"):
                d_residuals['states'] = gmres(self.state_jac, d_outputs['states'], x0=d_residuals['states'])[0]
            else:
                d_residuals['states'] = gmres(self.state_jac, d_outputs['states'], x0=d_residuals['states'], atol='legacy')[0]

p = om.Problem()
indeps = p.model.add_subsystem('indeps', om.IndepVarComp(), promotes_outputs=['a', 'b', 'c'])
indeps.add_output('a', 1.)
indeps.add_output('b', 4.)
indeps.add_output('c', 1.)
p.model.add_subsystem('quad', QuadraticComp(), promotes_inputs=['a', 'b', 'c'], promotes_outputs=['states'])

p.model.add_design_var('a', cache_linear_solution=True)
p.model.add_constraint('states', upper=10)


p.setup(mode='fwd')
p.run_model()

print(p['states'])

derivs = p.compute_totals(of=['states'], wrt=['a'])
print(derivs['states', 'a'])

p['a'] = 4
derivs = p.compute_totals(of=['states'], wrt=['a'])
print(derivs['states', 'a'])

以上代码输出如下：

[-0.26794919 -4.        ]
incoming initial guess [0. 0.]
[[-0.02072594]
 [ 4.        ]]
incoming initial guess [0. 0.]
[[-0.02072594]
 [ 4.        ]]

从这个例子的输出来看，线性猜测的初始猜测似乎并没有被实际更新。我错过了什么吗？我也试过运行将 cache_linear_solution 设置为 False 的代码，结果似乎是一样的。

Answer 1

目前，线性解决方案的缓存仅在驱动程序运行期间计算总导数时发生，因此如果您想检查以确保它在优化期间发生（在 run_driver调用），更改

derivs = p.compute_totals(of=['states'], wrt=['a'])

到

derivs = p.driver._compute_totals(of=['states'], wrt=['a'], global_names=False)

当我使用您的代码执行此操作时，我得到以下输出：

[-0.26794919 -4.        ]
incoming initial guess [0. 0.]
[[-0.02072594]
 [ 4.        ]]
incoming initial guess [-0.02072594  4.        ]
[[-0.02072594]
 [ 4.        ]]

请注意，仅当您为 of 和 wrt 变量使用提升的名称时才需要 global_names=False arg。

我将更新我们的示例代码以反映执行此操作的正确方法。

OpenMDAO cache_linear_solution 未更新初始猜测

OpenMDAO cache_linear_solution not updating initial guess

python

openmdao