The power of PySD, and its motivation for existence, is its ability to tie in to other models and analysis packages in the Python environment. In this section we’ll discuss how those connections happen.

## Replacing model components with more complex objects¶

In the last section we saw that a parameter could take on a single value, or a series of values over time, with PySD linearly interpolating between the supplied time-series values. Behind the scenes, PySD is translating that constant or time-series into a function that then goes on to replace the original component in the model. For instance, in the teacup example, the room temperature was originally a function defined through parsing the model file as something similar to:

def room_temperature():
return 75


However, when we made the room temperature something that varied with time, PySD replaced this function with something like:

def room_temperature():
return np.interp(t, series.index, series.values)


This drew on the internal state of the system, namely the time t, and the time-series data series that that we wanted to variable to represent. This process of substitution is available to the user, and we can replace functions ourselves, if we are careful.

Because PySD assumes that all components in a model are represented as functions taking no arguments, any component that we wish to modify must be replaced with a function taking no arguments. As the state of the system and all auxiliary or flow methods are public, our replacement function can call these methods as part of its internal structure.

In our teacup example, suppose we didn’t know the functional form for calculating the heat lost to the room, but instead had a lot of data of teacup temperatures and heat flow rates. We could use a regression model (here a support vector regression from Scikit-Learn) in place of the analytic function:

from sklearn.svm import SVR
regression = SVR()
regression.fit(X_training, Y_training)


Once the regression model is fit, we write a wrapper function for its predict method that accesses the input components of the model and formats the prediction for PySD:

def new_heatflow_function():
""" Replaces the original flowrate equation
with a regression model"""
tea_temp = model.components.teacup_temperature()
room_temp = model.components.room_temperature()
return regression.predict([room_temp, tea_temp])[0]


We can substitute this function directly for the heat_loss_to_room model component:

model.components.heat_loss_to_room = new_heatflow_function


## Supplying additional arguments to the integrator¶

the run() function’s argument intg_kwargs is a pass-through for keyword arguments to scipy’s odeint function, and as such can take on any of the keywords that odeint recognizes.