Specifying initial conditions

When calling ODEIntegrator, there are two ways of specifying the initial conditions.

1. Fixed initial conditions

If the initial conditions are fixed, the simplest way to specify them is to pass them in when calling ODEIntegrator:

import numpy as np
import matplotlib.pyplot as plt

from openmdao.api import Problem

from ozone.api import ODEIntegrator
from ozone.tests.ode_function_library.getting_started_ode_func \
    import GettingStartedODEFunction

ode_function = GettingStartedODEFunction()
formulation = 'solver-based'
method_name = 'RK4'
times = np.linspace(0., 3., 101)

# Here, initial_conditions is passed in.
initial_conditions = {'y': 1.}

integrator = ODEIntegrator(ode_function, formulation, method_name,
    times=times, initial_conditions=initial_conditions)

prob = Problem(model=integrator)
prob.setup(check=False)
prob.run_model()

plt.plot(prob['times'], prob['state:y'][:, 0])
plt.xlabel('t')
plt.ylabel('y')
plt.show()

2. Variable initial conditions

If the initial conditions vary during optimization, they must be connected from an external component:

import numpy as np
import matplotlib.pyplot as plt

from openmdao.api import Problem, IndepVarComp

from ozone.api import ODEIntegrator
from ozone.tests.ode_function_library.getting_started_ode_func \
    import GettingStartedODEFunction

ode_function = GettingStartedODEFunction()
formulation = 'solver-based'
method_name = 'RK4'
times = np.linspace(0., 3., 101)

integrator = ODEIntegrator(ode_function, formulation, method_name,
    times=times)

# Below, the initial condition is connected from an external component.
prob = Problem()
prob.model.add_subsystem('initial_conditions_comp', IndepVarComp('y0', 1.))
prob.model.add_subsystem('integrator_group', integrator)
prob.model.connect('initial_conditions_comp.y0', 'integrator_group.initial_condition:y')
prob.setup(check=False)
prob.run_model()

plt.plot(prob['integrator_group.times'], prob['integrator_group.state:y'][:, 0])
plt.xlabel('t')
plt.ylabel('y')
plt.show()