Getting Started

The workflow for DataDrivenDiffEq.jl is similar to other SciML packages. You start by defining a DataDrivenProblem and then dispatch on the solve command to return a DataDrivenSolution.

Here is an outline of the required elements and choices:

• Define a DataDrivenProblem using your data.
• Optional: Choose a Basis.
• solve the problem.

using DataDrivenDiffEq
using ModelingToolkit
using LinearAlgebra
using DataDrivenSparse

Generate a test problem

f(u) = u .^ 2 .+ 2.0u .- 1.0
X = randn(1, 100);
Y = reduce(hcat, map(f, eachcol(X)));

Create a problem from the data

problem = DirectDataDrivenProblem(X, Y, name = :Test)

Direct DataDrivenProblem{Float64} Test in 1 dimensions and 100 samples

Choose a basis

@variables u
basis = Basis(monomial_basis([u], 2), [u])

Model ##Basis#320 with 3 equations
States : u
Independent variable: t
Equations
φ₁ = 1
φ₂ = u
φ₃ = u^2

Solve the problem, using the solver of your choosing

res = solve(problem, basis, STLSQ())

"DataDrivenSolution{Float64}" with 1 equations and 3 parameters.
Returncode: Success
Residual sum of squares: 3.94138999850611e-18

Copy-Pasteable Code

using DataDrivenDiffEq
using ModelingToolkit
using LinearAlgebra
using DataDrivenSparse

f(u) = u .^ 2 .+ 2.0u .- 1.0
X = randn(1, 100);
Y = reduce(hcat, map(f, eachcol(X)));

problem = DirectDataDrivenProblem(X, Y, name = :Test)

@variables u
basis = Basis(monomial_basis([u], 2), [u])
println(basis) # hide

res = solve(problem, basis, STLSQ())
println(res) # hide

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