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https://github.com/SciML/DataDrivenDiffEq.jl

Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization
https://github.com/SciML/DataDrivenDiffEq.jl

differential-equations julia ode scientific-machine-learning sciml

Last synced: 3 months ago
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Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization

Host: GitHub
URL: https://github.com/SciML/DataDrivenDiffEq.jl
Owner: SciML
License: mit
Created: 2019-10-04T13:57:06.000Z (about 5 years ago)
Default Branch: master
Last Pushed: 2024-04-02T00:40:45.000Z (7 months ago)
Last Synced: 2024-04-14T01:46:51.441Z (7 months ago)
Topics: differential-equations, julia, ode, scientific-machine-learning, sciml
Language: Julia
Homepage: https://docs.sciml.ai/DataDrivenDiffEq/stable/
Size: 50.6 MB
Stars: 397
Watchers: 20
Forks: 54
Open Issues: 79
Metadata Files:
- Readme: README.md
- License: LICENSE

Awesome Lists containing this project

awesome-sciml - SciML/DataDrivenDiffEq.jl: Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization

README

        # 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://docs.sciml.ai/DataDrivenDiffEq/stable/). Use the

[in-development documentation](https://docs.sciml.ai/DataDrivenDiffEq/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 DataDrivenSparse

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

ddprob = DataDrivenProblem(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, 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

```

![](LorenzResult.png)