An arXiv preprint introduces PEtab SciML, an interoperable format for scientific machine-learning problems that estimate mechanistic and machine-learning parameters together from time-series data. The proposal is aimed at making the full problem specification portable: it describes the neural network, the ordinary differential-equation model and the links between them in a form that can be used across software ecosystems. The paper presents the format alongside a reference library, importers, tests and real-data benchmarks, framing the package as infrastructure for specifying, sharing and using scientific machine-learning models.
A language for the model itself
PEtab SciML defines several connected parts for that exchange. A YAML neural-network exchange format describes the network; a hybridization table, used together with a mapping table, describes how machine learning connects to the mechanistic model; and an HDF5 array format handles high-dimensional machine-learning data. In effect, the proposal separates the model components from the tables and arrays needed to connect them, giving implementations a common description of a hybrid model.
That structure matters because the machine-learning component is not treated as an isolated add-on. The format is designed to describe the neural network, its interaction with the ODE model and the data needed by the machine-learning part within the same exchange framework. The central idea is a shared representation that can travel between tools and programming-language ecosystems.
Where machine learning enters
The arrangement can vary. Machine learning may sit upstream of the ODE, operate inside the equation’s right-hand side—the part that determines how the system changes over time—or appear in the observation mapping that connects model output to measurements. A single problem can include multiple hybridizations. This means the format can describe different roles for machine learning rather than imposing one fixed neural-network-and-equation layout.
The reported feature set also reaches beyond the core link between a network and an equation. It includes multiple observables or experimental conditions, drug-dosing events and pre-equilibration. The specification can also represent parameter priors for Bayesian inference and a range of measurement-noise models, allowing those parts of a time-series problem to be recorded alongside the model itself.
A defined boundary
PEtab SciML has a clear boundary. It targets explicit ordinary differential equation structures as hard constraints. It does not cover physics-informed neural networks. The proposal is therefore specific about the kind of hybrid model it is intended to exchange: one in which the mechanistic ODE structure is explicit and remains part of the problem specification.
Software that carries the specification
The reported software ecosystem includes a reference Python library, Python/JAX and Julia support through AMICI and PEtab.jl, and real-data benchmarks. An AMICI import is described as generating optimized differentiable modules and scalable automatic differentiation for gradients of both mechanistic and machine-learning parameters during parameter-estimation solving. In this setting, automatic differentiation is a software technique for calculating how results change as those parameters change.
Training choices are represented in the Python library as transformations of a problem. The paper lists curriculum learning, multiple shooting and curriculum multiple shooting. In the paper’s description, those approaches are handled as part of the problem representation, putting the training setup alongside the model definition rather than treating it as a separate undocumented detail.
Tests and real-data cases
Interoperability is tested through a public test suite used continuously to check importer correctness across the documented feature space. It covers the supported hybridizations, neural-network architectures and PEtab features. An importer is the software component that reads the exchange representation for use in another environment, so the preprint presents these tests as a public check that the documented features are being handled correctly.
The paper also provides real-data PEtab SciML benchmarks spanning different hybridizations and applications from intracellular modeling to epidemiology. These benchmarks give researchers shared problems on which to exercise the format, importers and training transformations. Alongside the test suite, they form part of the authors’ broader framing of PEtab SciML as a resource for sharing and using models across programming languages.
An infrastructure proposal
Taken together, the format, library, importers and benchmark collection support an infrastructure-focused contribution. The authors frame them as programming-language-independent resources for specifying, sharing and using scientific machine-learning models. The emphasis is on how a hybrid model is represented, how software can import that representation and how researchers can work with shared tests and benchmark problems around it.
What readers can inspect
The documentation, Python library, test suite, benchmark collection, AMICI and PEtab.jl are reported as available. AMICI and PEtab.jl are identified as open-source packages. The proposal is therefore accompanied by a reference implementation and public resources for checking and exercising the exchange format, rather than being confined to a description of the format alone.
Support is reported from the Deutsche Forschungsgemeinschaft, European Union ERC programs, the University of Bonn, the Swedish Research Council and the Francis Crick Institute’s core-funding partners. The paper says funders had no role in study design, data collection or analysis, interpretation, manuscript writing or the publication decision. The authors declare no competing interests.
Paper data and sources
Original title: PEtab SciML: an exchange format for specifying and training dynamic scientific machine learning models
Authors: Sebastian Persson, Branwen Snelling, Maren Philipps et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
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