  Complex systems in science and engineering sometimes exhibit behavior that
changes across different regimes. Traditional global models struggle to capture
the full range of this complex behavior, limiting their ability to accurately
represent the system. In response to this challenge, we propose a novel
competitive learning approach for obtaining data-driven models of physical
systems. The primary idea behind the proposed approach is to employ dynamic
loss functions for a set of models that are trained concurrently on the data.
Each model competes for each observation during training, allowing for the
identification of distinct functional regimes within the dataset. To
demonstrate the effectiveness of the learning approach, we coupled it with
various regression methods that employ gradient-based optimizers for training.
The proposed approach was tested on various problems involving model discovery
and function approximation, demonstrating its ability to successfully identify
functional regimes, discover true governing equations, and reduce test errors.
