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.

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