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Complex systems in science and engineering sometimes exhibit behavior thatchanges across different regimes. Traditional global models struggle to capturethe full range of this complex behavior, limiting their ability to accuratelyrepresent the system. In response to this challenge, we propose a novelcompetitive learning approach for obtaining data-driven models of physicalsystems. The primary idea behind the proposed approach is to employ dynamicloss functions for a set of models that are trained concurrently on the data.Each model competes for each observation during training, allowing for theidentification of distinct functional regimes within the dataset. Todemonstrate the effectiveness of the learning approach, we coupled it withvarious regression methods that employ gradient-based optimizers for training.The proposed approach was tested on various problems involving model discoveryand function approximation, demonstrating its ability to successfully identifyfunctional regimes, discover true governing equations, and reduce test errors.

A Competitive Learning Approach for Specialized Models: A Solution for Complex Physical Systems with Distinct Functional Regimes