This submodule contains tools used to perform inference on ordinary differential equations.

class pymc3.ode.DifferentialEquation(func, times, *, n_states, n_theta, t0=0)

Specify an ordinary differential equation

\[\dfrac{dy}{dt} = f(y,t,p) \quad y(t_0) = y_0\]

Function specifying the differential equation. Must take arguments y (n_states,), t (scalar), p (n_theta,)


Array of times at which to evaluate the solution of the differential equation.


Dimension of the differential equation. For scalar differential equations, n_states=1. For vector valued differential equations, n_states = number of differential equations in the system.


Number of parameters in the differential equation.


Time corresponding to the initial condition


def odefunc(y, t, p):
    #Logistic differential equation
    return p[0] * y[0] * (1 - y[0])

times = np.arange(0.5, 5, 0.5)

ode_model = DifferentialEquation(func=odefunc, times=times, n_states=1, n_theta=1, t0=0)
grad(inputs, output_grads)

Construct a graph for the gradient with respect to each input variable.

Each returned Variable represents the gradient with respect to that input computed based on the symbolic gradients with respect to each output. If the output is not differentiable with respect to an input, then this method should return an instance of type NullType for that input.

inputslist of Variable

The input variables.

output_gradslist of Variable

The gradients of the output variables.

gradslist of Variable

The gradients with respect to each Variable in inputs.

make_node(y0, theta)

Construct an Apply node that represent the application of this operation to the given inputs.

This must be implemented by sub-classes.

node: Apply

The constructed Apply node.

perform(node, inputs_storage, output_storage)

Calculate the function on the inputs and put the variables in the output storage.


The symbolic Apply node that represents this computation.


Immutable sequence of non-symbolic/numeric inputs. These are the values of each Variable in node.inputs.

output_storagelist of list

List of mutable single-element lists (do not change the length of these lists). Each sub-list corresponds to value of each Variable in node.outputs. The primary purpose of this method is to set the values of these sub-lists.


A tuple containing the values of each entry in __props__.


The output_storage list might contain data. If an element of output_storage is not None, it has to be of the right type, for instance, for a TensorVariable, it has to be a NumPy ndarray with the right number of dimensions and the correct dtype. Its shape and stride pattern can be arbitrary. It is not guaranteed that such pre-set values were produced by a previous call to this Op.perform; they could’ve been allocated by another Op’s perform method. A Op is free to reuse output_storage as it sees fit, or to discard it and allocate new memory.