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Problems

DataDrivenDiffEq.DataDrivenProblem — Type
struct DataDrivenProblem{dType, cType, probType} <: DataDrivenDiffEq.AbstractDataDrivenProblem{dType, cType, probType}

The DataDrivenProblem defines a general estimation problem given measurements, inputs and (in the near future) observations. Three construction methods are available:

  • DirectDataDrivenProblem for direct mappings
  • DiscreteDataDrivenProblem for time discrete systems
  • ContinuousDataDrivenProblem for systems continuous in time

where all are aliases for constructing a problem.

Fields

  • X: State measurements

  • t: Time measurements (optional)

  • DX: Differential state measurements (optional); Used for time continuous problems

  • Y: Output measurements (optional); Used for direct problems

  • U: Input measurements (optional); Used for non-autonomous problems

  • p: Parameters associated with the problem (optional)

  • name: Name of the problem

Signatures

Example

X, DX, t = data...

# Define a discrete time problem
prob = DiscreteDataDrivenProblem(X)

# Define a continuous time problem without explicit time points
prob = ContinuousDataDrivenProblem(X, DX)

# Define a continuous time problem without explicit derivatives
prob = ContinuousDataDrivenProblem(X, t)

# Define a discrete time problem with an input function as a function
input_signal(u,p,t) = t^2
prob = DiscreteDataDrivenProblem(X, t, input_signal)
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Defining a Problem

Problems of identification, estimation, or inference are defined by data. These data contain at least measurements of the states X, which would be sufficient to describe a [DiscreteDataDrivenProblem](@ref) with unit time steps similar to the first example on dynamic mode decomposition. Of course, we can extend this to include time points t, control signals U or a function describing those u(x,p,t). Additionally, any parameters p known a priori can be included in the problem. In practice, this looks like:

problem = DiscreteDataDrivenProblem(X)
problem = DiscreteDataDrivenProblem(X, t)
problem = DiscreteDataDrivenProblem(X, t, U)
problem = DiscreteDataDrivenProblem(X, t, U, p = p)
problem = DiscreteDataDrivenProblem(X, t, (x, p, t) -> u(x, p, t))

Similarly, a ContinuousDataDrivenProblem would need at least measurements and time-derivatives (X and DX) or measurements, time information and a way to derive the time derivatives(X, t and a Collocation method). Again, this can be extended by including a control input as measurements or a function and possible parameters:

# Using available data
problem = ContinuousDataDrivenProblem(X, DX)
problem = ContinuousDataDrivenProblem(X, t, DX)
problem = ContinuousDataDrivenProblem(X, t, DX, U, p = p)
problem = ContinuousDataDrivenProblem(X, t, DX, (x, p, t) -> u(x, p, t))

# Using collocation
problem = ContinuousDataDrivenProblem(X, t, InterpolationMethod())
problem = ContinuousDataDrivenProblem(X, t, GaussianKernel())
problem = ContinuousDataDrivenProblem(X, t, U, InterpolationMethod())
problem = ContinuousDataDrivenProblem(X, t, U, GaussianKernel(), p = p)

You can also directly use a DESolution as an input to your DataDrivenProblem:

problem = DataDrivenProblem(sol; kwargs...)

which evaluates the function at the specific timepoints t using the parameters p of the original problem instead of using the interpolation. If you want to use the interpolated data, add the additional keyword use_interpolation = true.

An additional type of problem is the DirectDataDrivenProblem, which does not assume any kind of causal relationship. It is defined by X and an observed output Y in addition to the usual arguments:

problem = DirectDataDrivenProblem(X, Y)
problem = DirectDataDrivenProblem(X, t, Y)
problem = DirectDataDrivenProblem(X, t, Y, U)
problem = DirectDataDrivenProblem(X, t, Y, p = p)
problem = DirectDataDrivenProblem(X, t, Y, (x, p, t) -> u(x, p, t), p = p)

Concrete Types

DataDrivenDiffEq.ContinuousDataDrivenProblem — Function

A time continuous DataDrivenProblem useable for problems of the form f(x,p,t,u) ↦ dx/dt.

ContinuousDataDrivenProblem(X, DX; kwargs...)

Automatically constructs derivatives via an additional collocation method, which can be either a collocation or an interpolation from DataInterpolations.jl wrapped by an InterpolationMethod.

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Datasets

DataDrivenDiffEq.DataDrivenDataset — Type
struct DataDrivenDataset{N, U, C} <: DataDrivenDiffEq.AbstractDataDrivenProblem{N, U, C}

A collection of DataDrivenProblems used to concatenate different trajectories or experiments.

Can be called with either a NTuple of problems or a NamedTuple of NamedTuples. Similar to the DataDrivenProblem, it has three constructors available:

  • DirectDataset for direct problems
  • DiscreteDataset for discrete problems
  • ContinuousDataset for continuous problems

Fields

  • name: Name of the dataset

  • probs: The problems

  • sizes: The length of each problem - for internal use

Signatures

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A DataDrivenDataset collects several DataDrivenProblems of the same type but treats them as a union for system identification.

Concrete Types

DataDrivenDiffEq.ContinuousDataset — Function

A time continuous DataDrivenDataset useable for problems of the form f(x,p,t,u) ↦ dx/dt.

ContinuousDataset(s; name, collocation, kwargs...)

Automatically constructs derivatives via an additional collocation method, which can be either a collocation or an interpolation from DataInterpolations.jl wrapped by an InterpolationMethod provided by the collocation keyword argument.

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API

These methods are defined for DataDrivenProblems, but might be useful for developers.

DataDrivenDiffEq.is_valid — Function
is_valid(x)

Checks if a DataDrivenProblem is valid by checking if the data contains NaN, Inf and if the number of measurements is consistent.

Example

is_valid(problem)
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