# InformationOperator¶

class probnum.diffeq.odefilter.information_operators.InformationOperator(input_dim, output_dim)

Bases: ABC

Information operators used in probabilistic ODE solvers.

ODE solver-related information operators gather information about whether a state or function solves an ODE. More specifically, an information operator maps a sample from the prior distribution that is also an ODE solution to the zero function.

Consider the following example. For an ODE

$\dot y(t) - f(t, y(t)) = 0,$

and a $$\nu$$ times integrated Wiener process prior, the information operator maps

$\mathcal{Z}: [t, (Y_0, Y_1, ..., Y_\nu)] \mapsto Y_1(t) - f(t, Y_0(t)).$

(Recall that $$Y_j$$ models the j th derivative of Y_0 for given prior.) If $$Y_0$$ solves the ODE, $$\mathcal{Z}(Y)(t)$$ is zero for all $$t$$.

Information operators are used to condition prior distributions on solving a numerical problem. This happens by conditioning the prior distribution $$Y$$ on $$\mathcal{Z}(Y)(t_n)=0$$ on time-points $$t_1, ..., t_n, ..., t_N$$ ($$N$$ is usually large). Therefore, they are one important component in a probabilistic ODE solver.

Methods Summary

 __call__(t, x) Call self as a function. as_transition([noise_fun]) jacobian(t, x)

Methods Documentation

Parameters
abstract __call__(t, x)[source]

Call self as a function.

Parameters
Return type

ndarray

as_transition(noise_fun=None)[source]
Parameters

noise_fun (Optional[RandomVariable]) –

jacobian(t, x)[source]
Parameters
Return type

ndarray