HYCO: A Formalism for Hybrid-Cooperative PDE Modelling
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866909037218496512 |
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| author | Liverani, Lorenzo Zuazua, Enrique |
| author_facet | Liverani, Lorenzo Zuazua, Enrique |
| contents | 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 . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23859 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | HYCO: A Formalism for Hybrid-Cooperative PDE Modelling Liverani, Lorenzo Zuazua, Enrique Optimization and Control Numerical Analysis 00A71, 35R30, 41A27, 68T07, 91A12 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 . |
| title | HYCO: A Formalism for Hybrid-Cooperative PDE Modelling |
| topic | Optimization and Control Numerical Analysis 00A71, 35R30, 41A27, 68T07, 91A12 |
| url | https://arxiv.org/abs/2602.23859 |