Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization
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Started In
October 2019

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

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

## Quick Demonstration

```## Generate some data by solving a differential equation
########################################################
using ModelingToolkit
using OrdinaryDiffEq
using LinearAlgebra

# Create a test problem
function lorenz(u, p, t)
x, y, z = u

ẋ = 10.0 * (y - x)
ẏ = x * (28.0 - z) - y
ż = x * y - (8 / 3) * z
return [ẋ, ẏ, ż]
end

u0 = [1.0; 0.0; 0.0]
tspan = (0.0, 100.0)
dt = 0.1
prob = ODEProblem(lorenz, u0, tspan)
sol = solve(prob, Tsit5(), saveat = dt)

## Start the automatic discovery

@variables t x(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 Result
Solution with 3 equations and 7 parameters.
Returncode: success
Sparsity: 7.0
L2 Norm Error: 26.7343984476783
AICC: 1.0013570199499398

Model ##Basis#366 with 3 equations
States : x(t) y(t) z(t)
Parameters : 7
Independent variable: t
Equations
Differential(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
`````` ### Required Packages

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