Date: Tue. September 23, 2025
Event: FAU MoD Workshop
Event type: On-site / Online
Organized by: FAU MoD, the Research Center for Mathematics of Data at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)

Session 01: HYCO: Hybrid-Cooperative Learning for PDEs
Speaker: Prof. Dr. Lorenzo Liverani
Affiliation: FAU MoD, Research Center for Mathematics of Data | FAU DCN-AvH at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)

In this talk, I will present the Hybrid-Cooperative Learning strategy (HYCO), a modeling framework that iteratively integrates physics-based and data-driven models through a mutual regularization mechanism. Unlike traditional approaches that impose physical constraints directly on synthetic models, HYCO treats the physical and synthetic components as co-trained agents, nudging them towards mutual agreement. This cooperative learning scheme is naturally parallelizable and improves robustness to noise as well as to sparse or heterogeneous data. Through several numerical experiments on both static and time-dependent problems, I will demonstrate that HYCO is a promising architecture, outperforming classical physics-based and data-driven methods and recovering accurate solutions and model parameters even under ill-posed conditions. This is ongoing work with E. Zuazua and M. Steynberg.

See more details of this talk at:

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