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arXiv · 2602.23859

HYCO: A Formalism for Hybrid-Cooperative PDE Modelling

Lorenzo Liverani·Enrique Zuazua
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Abstract

We present Hybrid-Cooperative Learning (HYCO), a hybrid modeling framework that integrates physics-based and data-driven models through mutual regularization. Unlike traditional approaches that impose physical constraints directly on synthetic models, HYCO treats both components as co-trained agents nudged toward agreement. This cooperative scheme is naturally parallelizable and demonstrates robustness to sparse and noisy data. Numerical experiments on static and time-dependent benchmark problems show that HYCO can recover accurate solutions and model parameters under ill-posed conditions. The framework admits a game-theoretic interpretation as a Nash equilibrium problem, enabling alternating optimization. This paper is based on the extended preprint: arXiv:2509.14123 .

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Lorenzo Liverani, Enrique Zuazua. 2026-02-27. HYCO: A Formalism for Hybrid-Cooperative PDE Modelling. https://arxiv.org/abs/2602.23859

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