Objective
Classical first principles (FP) models have long been the foundation for studying temporal phenomena in science and engineering, but growing system complexity leads to prohibitive computational costs and accuracy, reducing simplifications. Machine learning (ML) methods have consequently flourished, often enabling more efficient predictions of future system behavior. Yet ML lacks FP’s mechanistic interpretability and typically requires large datasets. Project LEO builds on the critical insight that linear evolution operators underlie both approaches. By representing complex nonlinear systems as linear dynamics in suitable function spaces, these operators theoretically enable the extraction of global system properties from FP equations, which are key to scientific understanding. Yet, despite their recognized importance, the methodological foundations and learning theory of these operators remain underdeveloped. LEO will establish a bidirectional theoretical framework that unites the strengths of ML and FP models, paving the way for efficient and reliable algorithms for representation and operator learning. Achieving this ambitious goal requires overcoming substantial theoretical and practical challenges. Our approach builds on firm statistical learning theory foundations, within which we will develop learning guarantees quantifying the reliability and efficiency of our algorithms. Furthermore, LEO’s framework will enable robust inference and interpretable representations of system dynamics, capturing phenomena such as critical transitions in atomistic simulations or climate regime shifts. Our algorithms will be showcased on two distinct applications, where collaboration with domain experts will support evaluation of inferred representations and properties, guiding algorithm development in line with the project’s bidirectional approach. Finally, LEO will deliver open-source software, making our algorithms accessible to the research community, maximizing impact.
Fields of science (EuroSciVoc)
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2025-ADG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
16163 Genova
Italy
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.