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Learning linear evolution operators: a bidirectional approach

Objectif

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.

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Mots‑clés

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Régime de financement

HORIZON-ERC - HORIZON ERC Grants

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Appel à propositions

(s’ouvre dans une nouvelle fenêtre) ERC-2025-ADG

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Institution d’accueil

FONDAZIONE ISTITUTO ITALIANO DI TECNOLOGIA
Contribution nette de l'UE
€ 2 308 625,00
Coût total
Aucune donnée

Bénéficiaires (1)