https://github.com/augustinas1/datadrivendiffeq.jl

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

https://github.com/augustinas1/datadrivendiffeq.jl

Repository

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

https://github.com/augustinas1/DataDrivenDiffEq.jl/blob/master/

# DataDrivenDiffEq.jl

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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](https://datadriven.sciml.ai/stable/). Use the
[in-development documentation](https://datadriven.sciml.ai/dev/) for the version of
the documentation which contains the un-released features.

## Quick Demonstration

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

using LinearAlgebra

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

    x = 10.0*(y - x)
    y = x*(28.0-z) - y
    z = x*y - (8/3)*z
    return [x, y, z]
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, progress = true)


## Start the automatic discovery
ddprob = ContinuousDataDrivenProblem(sol)

@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, normalize = true)
print(ddsol, Val{true})
```

```
Explicit Result
Solution with 3 equations and 7 parameters.
Returncode: sucess
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)) = p*x(t) + p*y(t)
Differential(t)(y(t)) = p*x(t) + p*y(t) + p*x(t)*z(t)
Differential(t)(z(t)) = p*z(t) + p*x(t)*y(t)

Parameters:
   p : -10.0
   p : 10.0
   p : 28.0
   p : -1.0
   p : -1.0
   p : 1.0
   p : -2.7
```

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