A data format for scientific machine learning

PEtab SciML is a table-based data format for creating training (parameter estimation) problems for scientific machine learning (SciML) models that combine machine learning and mechanistic ordinary differential equation (ODE) models.

Extending the PEtab format for mechanistic ODE models, PEtab SciML provides a human readable, reproducible way to specify SciML training problems across diverse scenarios, in a format directly importable by downstream tools. The main aspects enabling this are:

• Flexible hybridization. Machine learning (ML) and ODE models can be combined in three ways: (1) ML within the ODE dynamics (includes Neural ODEs), (2) ML in the observable/measurement model linking simulations to data, and (3) ML upstream of the ODE, mapping high-dimensional inputs (e.g., images) to ODE model parameters.
• Import across ecosystems. PEtab SciML problems can be imported into state-of-the-art toolboxes for dynamic-model training in Julia (PEtab.jl) and Python/JAX (AMICI).
• Broad support for ML architectures. A diverse set of ML architectures can be specified via an exchangeable PEtab SciML YAML format (supports export from PyTorch modules), or via importer-specific libraries (e.g., Lux.jl in PEtab.jl; Equinox in AMICI).
• Diverse model types. All model features of the PEtab format are supported, like models with partial observability, multiple simulation conditions, diverse noise models, and/or events.
• Efficient training strategies. With minimal user input, PEtab SciML problems can be rewritten at the PEtab abstraction level to be compatible with training strategies such as multiple shooting, curriculum learning, and regularization (e.g., of ML outputs).
• Thoroughly tested. An extensive test suite ensures importers produce correct and consistent output.
• Linting and helpers. The PEtab SciML Python library provides a linter and utility functions for creating common problem types (e.g., Neural ODEs) and transformations (e.g., rewriting a PEtab problem for multiple-shooting training).

The PEtab SciML Python3 helper library can be installed with:

pip install petab-sciml

Information on features and tutorials can be found in the online documentation.