# DataDriven Approach for recovering DAE system of governing equations

Can I know if data driven recovery of governing equations that can be a DAE system is possible with DMD or SINDy approach in DataDrivenDiffEq.jl? I have referred the examples in the documentation of DataDrivenDiffEq.jl but but couldn’t find any on DAE. Any possible help is appreciated…

The iSINDy (implicit SINDy) method can do it.

Thankyou Chris.

Yeah… I do look into it. But the code given in the documentation isn’t working fine with me. The trouble is with trying to create a simulation model with the obtained result. These are the package specifications I use.

Julia 1.7.1
DifferentialEquations v7.5.0
Interpolations v0.14.6
ModelingToolkit v8.27.0
Plots v1.35.3

Below is the code and corresponding error message I received.

``````using DataDrivenDiffEq
using LinearAlgebra
using ModelingToolkit
using OrdinaryDiffEq

function slow_manifold(du, u, p, t)
du[1] = p[1] * u[1]
du[2] = p[2] * (u[2] - u[1]^2)
end

u0 = [3.0; -2.0]
tspan = (0.0, 5.0)
p = [-0.8; -0.7]

problem = ODEProblem(slow_manifold, u0, tspan, p)
solution = solve(problem, Tsit5(), saveat = 0.01);

@parameters t
@variables u[1:2](t)
Ψ = Basis([u; u[1]^2], u, independent_variable = t)
res = solve(prob, Ψ, DMDPINV(), digits = 1)
system = result(res)

sparse_res = solve(prob, Ψ, STLSQ(), digits = 1)

sparse_system = result(sparse_res)

parameter_map(res)

parameter_map(sparse_res)

@named sys = ODESystem(
equations(sparse_system),
get_iv(sparse_system),
states(sparse_system),
parameters(sparse_system)
);

``````
``````ArgumentError: p₁ is not a parameter.

Stacktrace:
[1] check_parameters(ps::Vector{Sym{Real, Base.ImmutableDict{DataType, Any}}}, iv::Sym{Real, Base.ImmutableDict{DataType, Any}})
@ ModelingToolkit C:\Users\Jisna\.julia\packages\ModelingToolkit\2nkY8\src\utils.jl:135
[2] ODESystem(tag::UInt64, deqs::Vector{Equation}, iv::Sym{Real, Base.ImmutableDict{DataType, Any}}, dvs::Vector{Term{Real, Base.ImmutableDict{DataType, Any}}}, ps::Vector{Sym{Real, Base.ImmutableDict{DataType, Any}}}, var_to_name::Dict{Any, Any}, ctrls::Vector{Any}, observed::Vector{Equation}, tgrad::Base.RefValue{Vector{Num}}, jac::Base.RefValue{Any}, ctrl_jac::Base.RefValue{Any}, Wfact::Base.RefValue{Matrix{Num}}, Wfact_t::Base.RefValue{Matrix{Num}}, name::Symbol, systems::Vector{ODESystem}, defaults::Dict{Any, Any}, torn_matching::Nothing, connector_type::Nothing, preface::Nothing, cevents::Vector{ModelingToolkit.SymbolicContinuousCallback}, devents::Vector{ModelingToolkit.SymbolicDiscreteCallback}, metadata::Nothing, tearing_state::Nothing, substitutions::Nothing, complete::Bool; checks::Bool)
@ ModelingToolkit C:\Users\Jisna\.julia\packages\ModelingToolkit\2nkY8\src\systems\diffeqs\odesystem.jl:136
[3] ODESystem(deqs::Vector{Equation}, iv::Num, dvs::Vector{Num}, ps::Vector{Sym{Real, Base.ImmutableDict{DataType, Any}}}; controls::Vector{Num}, observed::Vector{Equation}, systems::Vector{ODESystem}, name::Symbol, default_u0::Dict{Any, Any}, default_p::Dict{Any, Any}, defaults::Dict{Any, Any}, connector_type::Nothing, preface::Nothing, continuous_events::Nothing, discrete_events::Nothing, checks::Bool, metadata::Nothing)
@ ModelingToolkit C:\Users\Jisna\.julia\packages\ModelingToolkit\2nkY8\src\systems\diffeqs\odesystem.jl:197
[4] top-level scope
@ C:\Users\Jisna\.julia\packages\ModelingToolkit\2nkY8\src\systems\abstractsystem.jl:866
``````

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