DELPHI is an ERC Starting Grant led by Michael Arbel and scheduled to begin in October 2027. It is funded by the European Research Council (ERC) under the European Union’s Horizon Europe research and innovation programme.

Project description

Machine learning has thrived by training expressive models on large datasets, but is now shifting toward integrating prior knowledge—such as physical laws or structure—into the learning process. Many such problems can be formulated as implicitly constrained learning (ICL): a prediction model is subject to a partially known constraint whose unknown component is inferred by aligning predictions with data. ICL problems arise across domains, from enforcing physics in scientific models and planning from learned world models to accounting for hidden variables in causal-effect estimation. These settings remain difficult, particularly with expressive, over-parameterized models such as deep neural networks.

DELPHI will develop a principled and efficient methodological framework for ICL that can handle complex implicit constraints, ranging from auxiliary optimality conditions to partial differential equations and dynamical systems. Its goal is to connect theoretical, methodological, and practical advances in machine learning with problems in scientific discovery, causal reasoning, and decision-making.

Research questions

The programme will investigate:

  • How can a prediction model and the unknown component of a constraint be learned jointly, and under what assumptions is the resulting problem statistically identifiable?
  • Which optimization methods can handle constraints defined through optimality conditions, partial differential equations, or dynamical systems when the learned models are expressive neural networks?
  • When does incorporating an implicit constraint improve generalization and reliability compared with learning from data alone, in scientific inference, causal reasoning, or decision-making?

Project status

DELPHI is scheduled to start in October 2027. Its publications, software, and recruitment announcements will be added as they become public.

Contact

For current opportunities, please follow the application instructions. Positions associated with DELPHI will be announced once roles and timelines are formally confirmed.