Estimating parameter and function in an ODE model

Specific Domains Modelling & Simulations
1

Hi all,

I’m working on an ODE model where I want to infer a parameter μ and a function ϕ(t), and I’m looking for recommendations for tools or approaches in Julia to solve this problem. My dataset is small, with just 7 data points in the form (t, n).

The model is given by:

\frac{dn}{dt} = \phi(t) - \mu \, n(t), \quad n(t=0) = 0

I’m considering two possible approaches for modeling ϕ(t):

  1. Gaussian Process (GP) for a non-parametric approach.
  2. Neural Networks (NNs) to approximate ϕ(t), but with strong regularization given the limited data.

Which approach and related packages would you recommend in Julia for this problem?

Any guidance or relevant examples would be greatly appreciated!

Thanks in advance for your help!

2

See for example Parameter Estimation of Ordinary Differential Equations · SciMLSensitivity.jl

For your case here, I’d recommend using DataInterpolations.jl to represent the phi via a spline at a bunch of points, and differentiate w.r.t. those points.

3

Isn’t at least anything known/assumed about \phi(t)?

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