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Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization

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DataDrivenDiffEq.jl

DataDrivenDiffEq.jl is a package in the SciML ecosystem for data-driven differential equationstructural estimation and identification. These tools include automatically discovering equationsfrom data and using this to simulate perturbed dynamics.

For information on using the package,see the stable documentation. Use thein-development documentation for the version ofthe documentation which contains the un-released features.

Quick Demonstration

## Generate some data by solving a differential equation########################################################using DataDrivenDiffEqusing ModelingToolkitusing OrdinaryDiffEqusing DataDrivenSparseusing LinearAlgebra# Create a test problemfunctionlorenz(u, p, t)    x, y, z= u    ẋ=10.0* (y- x)    ẏ= x* (28.0- z)- y    ż= x* y- (8/3)* zreturn [ẋ, ẏ, ż]endu0= [1.0;0.0;0.0]tspan= (0.0,100.0)dt=0.1prob=ODEProblem(lorenz, u0, tspan)sol=solve(prob,Tsit5(), saveat= dt)## Start the automatic discoveryddprob=DataDrivenProblem(sol)@variables tx(t)y(t)z(t)u= [x; y; z]basis=Basis(polynomial_basis(u,5), u, iv= t)opt=STLSQ(exp10.(-5:0.1:-1))ddsol=solve(ddprob, basis, opt, options=DataDrivenCommonOptions(digits=1))println(get_basis(ddsol))

Explicit ResultSolution with 3 equations and 7 parameters.Returncode: successSparsity: 7.0L2 Norm Error: 26.7343984476783AICC: 1.0013570199499398Model ##Basis#366 with 3 equationsStates : x(t) y(t) z(t)Parameters : 7Independent variable: tEquationsDifferential(t)(x(t)) = p₁*x(t) + p₂*y(t)Differential(t)(y(t)) = p₃*x(t) + p₄*y(t) + p₅*x(t)*z(t)Differential(t)(z(t)) = p₇*z(t) + p₆*x(t)*y(t)Parameters:   p₁ : -10.0   p₂ : 10.0   p₃ : 28.0   p₄ : -1.0   p₅ : -1.0   p₆ : 1.0   p₇ : -2.7