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.

翻译：科学与工程中的复杂系统有时会在不同状态下表现出变化的行为。传统全局模型难以捕捉这种复杂行为的全貌，从而限制了其准确表征系统的能力。针对这一挑战，我们提出了一种新颖的竞争式学习方法，用于获取物理系统的数据驱动模型。该方法的核心思想是为一组同时基于数据训练的模型采用动态损失函数。在训练过程中，每个模型针对每个观测值进行竞争，从而能够识别数据集内不同的功能状态。为证明该学习方法的有效性，我们将其与多种采用梯度优化器训练的回归方法相结合。该方法在涉及模型发现与函数逼近的多种问题上进行了测试，结果表明它能够成功识别功能状态、发现真实控制方程并降低测试误差。