Sampling transitions

transition(
    sys::CoupledSDEs,
    x_i,
    x_f;
    radii,
    tmax,
    radius_directions,
    cut_start,
    kwargs...
) -> Tuple{Any, Any, Bool}

Generates a sample transition from point x_i to point x_f.

This function simulates sys in time, starting from initial condition x_i, until entering a ball of given radius around x_f. If a seed was given to sys the solver is initialized with this seed. To change the seed you can pass a new seed to the seed keyword.

Keyword arguments

• radii=(0.1, 0.1): radius of the ball around x_i and x_f, respectively
• tmax=1e3: maximum time until the simulation stops even x_f has not been reached
• radius_directions=1:length(sys.u): the directions in phase space to consider when calculating the radii rad_i and rad_f. Defaults to all directions. To consider only a subspace of state space, insert a vector of indices of the dimensions to be included.
• cut_start=true: if false, returns the whole trajectory up to the transition
• kwargs...: keyword arguments passed to CommonSolve.solve

Output

[path, times, success]

• path (Matrix): transition path (size [dim × N], where N is the number of time points)
• times (Vector): time values (since start of simulation) of the path points (size N)
• success (bool): if true, a transition occurred (i.e. the ball around x_f has been reached), else false

See also transitions, trajectory.

transitions(
    sys::CoupledSDEs,
    x_i,
    x_f;
    ...
) -> CriticalTransitions.TransitionEnsemble{_A, _B, EnsembleSolution{T, N, S}} where {_A, _B, T, N, S}
transitions(
    sys::CoupledSDEs,
    x_i,
    x_f,
    N::Int64;
    radii,
    tmax,
    Nmax,
    cut_start,
    radius_directions,
    show_progress,
    EnsembleAlg,
    kwargs...
) -> CriticalTransitions.TransitionEnsemble{_A, _B, EnsembleSolution{T, N, S}} where {_A, _B, T, N, S}

Generates an ensemble of N transition samples of sys from point x_i to point x_f. The transitions is by default simulated using threading. To sample the transitions in serial, GPU or Distributed enverionment, pass the desired SciMLBase.EnsembleAlgorithm to the EnsembleAlg algorithm.

Keyword arguments

• radii=(0.1, 0.1): radius of the ball around x_i and x_f, respectively
• Nmax: number of attempts before the algorithm stops even if less than N transitions occurred.
• tmax=1e3: maximum time when the simulation stops even x_f has not been reached
• radius_directions=1:length(sys.u): the directions in phase space to consider when calculating the radii rad_i and rad_f. Defaults to all directions. To consider only a subspace of state space, insert a vector of indices of the dimensions to be included.
• cut_start=true: if false, returns the whole trajectory up to the transition
• show_progress=true: shows a progress bar with respect to Nmax
• kwargs...: keyword arguments passed to CommonSolve.solve

See also transition.

Returns a TransitionEnsemble object.

struct TransitionEnsemble{SSS, T, ES}

Ensemble of transition paths between two points in a state space.

Fields

• paths::Vector: paths sampled from the transition process

• times::Array{Vector{T}, 1} where T: coresponsing times of the paths

• stats::CriticalTransitions.TransitionStatistics: statistics of the ensemble

• sciml_ensemble::Any: original ensemble solution of the SciML Ensemble problem

Constructors

TransitionEnsemble(sim, success_rate)

defined at /home/runner/work/CriticalTransitions.jl/CriticalTransitions.jl/src/trajectories/TransitionEnsemble.jl:55.

struct TransitionStatistics{T}

Statistics of the ensemble of transition paths between two points in a state space.

Fields

• success_rate::Any: success rate of the transition process

• residence_time::Any: mean residence time of the transition process

• transition_time::Any: mean transition time of the transition process

• rareness::Any: rareness of the transition process

Constructors

TransitionStatistics(sim, success_rate)

defined at /home/runner/work/CriticalTransitions.jl/CriticalTransitions.jl/src/trajectories/TransitionEnsemble.jl:23.