PerturbedStepSolver

class probnum.diffeq.perturbed.step.PerturbedStepSolver(rng, solver, noise_scale, perturb_function)

Bases: ODESolver

Probabilistic ODE solver based on random perturbation of the step-sizes.

Perturbs the steps accordingly and projects the solution back to the originally proposed time points. Proposed by Abdulle and Garegnani (2020) 1.

Parameters

• rng (Generator) – Random number generator.

• solver (WrappedScipyRungeKutta) – Currently this has to be a Runge-Kutta method based on SciPy.

• noise-scale – Scales the amount of noise that is introduced.

• perturb_function (Callable) – Defines how the stepsize is distributed. This can be either one of perturb_lognormal() or perturb_uniform() or any other perturbation function with the same signature.

• noise_scale (Union[float, Real, floating]) –

References

1

Abdulle, A. and Garegnani, G. Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration. Statistics and Computing. 2020.

Methods Summary

attempt_step(state, dt)	Perturb the original stopping point.
construct_with_lognormal_perturbation(rng, ...)
construct_with_uniform_perturbation(rng, ...)
initialize(ivp)	Initialise and reset the solver.
method_callback(state)	Call dense output after each step and store the interpolants.
perform_full_step(state, initial_dt)	Perform a full ODE solver step.
postprocess(odesol)	Process the ODESolution object before returning.
rvlist_to_odesol(times, rvs)	Create an ODESolution object.
solution_generator(ivp[, stop_at, callbacks])	Generate ODE solver steps.
solve(ivp[, stop_at, callbacks])	Solve an IVP.

Methods Documentation

attempt_step(state, dt)

Perturb the original stopping point.

Perform one perturbed step and project the solution back to the original stopping point.

Parameters

• state (ODESolverState) – Current state of the ODE solver.

• dt (Union[float, Real, floating]) – Step-size.

Returns

New state.

Return type

_odesolver_state.ODESolverState

classmethod construct_with_lognormal_perturbation(rng, solver, noise_scale)

Parameters

• rng (Generator) –

• solver (WrappedScipyRungeKutta) –

• noise_scale (Union[float, Real, floating]) –

classmethod construct_with_uniform_perturbation(rng, solver, noise_scale)

Parameters

• rng (Generator) –

• solver (WrappedScipyRungeKutta) –

• noise_scale (Union[float, Real, floating]) –

initialize(ivp)

Initialise and reset the solver.

method_callback(state)

Call dense output after each step and store the interpolants.

perform_full_step(state, initial_dt)

Perform a full ODE solver step.

This includes the acceptance/rejection decision as governed by error estimation and steprule.

postprocess(odesol)

Process the ODESolution object before returning.

rvlist_to_odesol(times, rvs)

Create an ODESolution object.

Parameters

• times (ndarray) –

• rvs (_RandomVariableList) –

solution_generator(ivp, stop_at=None, callbacks=None)

Generate ODE solver steps.

Parameters

• ivp (problems.InitialValueProblem) –

• stop_at (Iterable[FloatLike]) –

• callbacks (Optional[CallbackType]) –

solve(ivp, stop_at=None, callbacks=None)

Solve an IVP.

Parameters

• ivp (problems.InitialValueProblem) – Initial value problem.

• stop_at (Iterable[FloatLike]) – Time-points through which the solver must step. Optional. Default is None.

• callbacks (Optional[CallbackType]) – Callbacks to happen after every accepted step.