Recovery model Tsodyks and Markram with Sindy DataDrivenDiffEq.jl

Specific Domains Modelling & Simulations
1

Hello, is it possible to reconstruct the Tsodyks and Markram model using SINDY? If so, how do you correctly define candidates and what to do with such a nonlinearity as a function g (E, x, u, J, I0) = α * log (1.0 + exp ((J * u * x * E + I0) / α ))

Can someone share a code example where a model with a similar nonlinearity was restored?

Thanks for your help

@inbounds function TM(var, p, t)

    E,x, u = var;
    τ, τ_F, τ_D, U, J, I0, α = p;
    
    g(E, x, u, J, I0) = α * log( 1.0 + exp( (J * u * x * E + I0) / α ))

    du1 = (-E + g(E, x, u, J, I0)) / τ;
    du2 = (1 - x) / τ_D - u * E * x;
    du3 = U * E * (1 - u) - (u - U) / τ_F; 

    return SVector(du1, du2, du3)
end

function TM_params()
    τ = 13.0 / 1000.0
    τ_D = 200.0 / 1000.0
    τ_F = 1500.0 / 1000.0
    J = 3.07 
    U = 0.3
    α = 1.5
    I0 = -1.765
    return [τ, τ_F, τ_D, U, J, I0, α];
end
2

It would require a like term in the library for reconstruction. This kind of nonlinearity is better dealt with SymbolicRegression.jl rather than the linear symbolic regression tooling.

3

Thank you!