logistic_ode¶

probnum.problems.zoo.filtsmooth.logistic_ode(y0=None, timespan=(0.0, 2.0), step=0.1, params=(6.0, 1.0), initrv=None, evlvar=None, ek0_or_ek1=1, exclude_initial_condition=True, order=3, forward_implementation='classic', backward_implementation='classic')[source]¶

Filtering/smoothing setup for a probabilistic ODE solver for the logistic ODE.

This state space model assumes an integrated Brownian motion prior on the dynamics and constructs the ODE likelihood based on the vector field defining the logistic ODE.

Parameters

y0 (Optional[Union[np.ndarray, FloatLike]]) – Initial conditions of the Initial Value Problem
timespan (Tuple[FloatLike, FloatLike]) – Time span of the problem
params (Tuple[FloatLike, FloatLike]) – Parameters for the logistic ODE
initrv (Optional[randvars.RandomVariable]) – Initial random variable of the probabilistic ODE solver
evlvar (Optional[Union[np.ndarray, FloatLike]]) – See probnum.diffeq.ODEFilter
ek0_or_ek1 (IntLike) – See probnum.diffeq.ODEFilter
exclude_initial_condition (bool) – Whether the resulting regression problem should exclude (i.e. not contain) the initial condition of the ODE. Optional. Default is True, which means that the initial condition is omitted.
order (IntLike) – Order of integration for the Integrated Brownian Motion prior of the solver.
forward_implementation (str) – Implementation of the forward transitions inside prior and measurement model. Optional. Default is classic. For improved numerical stability, use sqrt.
backward_implementation (str) – Implementation of the backward transitions inside prior and measurement model. Optional. Default is classic. For improved numerical stability, use sqrt.
step (FloatLike) –

Returns

regression_problem – TimeSeriesRegressionProblem object with time points and zero-observations.
info – Dictionary containing additional information like the prior process.