Import PEtab SciML standard format

PEtab SciML extends the PEtab table-based standard for parameter estimation to support SciML parameter estimation problems [8]. PEtab.jl has full support for the PEtab SciML format, and this tutorial shows how to import such problems.

Input: a valid PEtab SciML problem

Tutorials on creating valid PEtab SciML problems are available in the PEtab SciML documentation. In this tutorial, the Lotka–Volterra UDE example from [19] is imported. The corresponding PEtab SciML files can be downloaded from here.

Briefly, the Lotka–Volterra SciML model describes interactions between a prey population and a predator population. In this SciML example, the interaction term in the original model is replaced by a neural network:

$$\begin{array}{rl}\frac{\mathrm{d}\mathrm{prey}}{\mathrm{d}t}& =\alpha \cdot \mathrm{prey}+\mathrm{NN}(\mathrm{prey},\mathrm{predator})[1]\\ \frac{\mathrm{d}\mathrm{predator}}{\mathrm{d}t}& =-\gamma \cdot \mathrm{predator}+\mathrm{NN}(\mathrm{prey},\mathrm{predator})[2]\end{array}$$

where NN(prey, predator) is a feed-forward neural network taking prey and predator abundances as input and returning a two-dimensional output.

PEtab SciML import

A PEtab SciML problem consists of multiple tables (e.g. measurements and parameter definitions), model files, and a YAML file that ties them together. To import the problem, only the path to the YAML file is needed. The first step is to load the ML models in the PEtab SciML problem:

using Lux, PEtab
# `path_yaml` depends on where the problem files are located
path_yaml = joinpath("lv_ude", "problem.yaml")
ml_models = MLModels(path_yaml)

MLModels with 1 models
  net1: (mode=simulation, parameters=51)

Then a PEtabModel and the corresponding PEtabODEProblem can be created:

petab_model = PEtabModel(path_yaml; ml_models = ml_models)
petab_prob = PEtabODEProblem(petab_model)

PEtabODEProblem lv_ude: 54 parameters to estimate
(for more statistics, call `describe(petab_prob)`)

As described in the SciML starter tutorial, petab_prob can then be used for downstream tasks such as simulation and model training.

References

1. L. Schmiester, Y. Schälte, F. T. Bergmann, T. Camba, E. Dudkin, J. Egert, F. Fröhlich, L. Fuhrmann, A. L. Hauber, S. Kemmer and others. PEtab—Interoperable specification of parameter estimation problems in systems biology. PLoS computational biology 17, e1008646 (2021).

2. C. Rackauckas, Y. Ma, J. Martensen, C. Warner, K. Zubov, R. Supekar, D. Skinner, A. Ramadhan and A. Edelman. Universal differential equations for scientific machine learning, arXiv preprint arXiv:2001.04385 (2020).