This paper addresses the challenge of overfitting in the learning of dynamical systems by introducing a novel approach for the generation of synthetic data, aimed at enhancing model generalization and robustness in scenarios characterized by data scarcity. Central to the proposed methodology is the concept of knowledge transfer from systems within the same class. Specifically, synthetic data is generated through a pre-trained meta-model that describes a broad class of systems to which the system of interest is assumed to belong. Training data serves a dual purpose: firstly, as input to the pre-trained meta model to discern the system's dynamics, enabling the prediction of its behavior and thereby generating synthetic output sequences for new input sequences; secondly, in conjunction with synthetic data, to define the loss function used for model estimation. A validation dataset is used to tune a scalar hyper-parameter balancing the relative importance of training and synthetic data in the definition of the loss function. The same validation set can be also used for other purposes, such as early stopping during the training, fundamental to avoid overfitting in case of small-size training datasets. The efficacy of the approach is shown through a numerical example that highlights the advantages of integrating synthetic data into the system identification process.

翻译：本文针对动态系统学习中的过拟合问题，提出了一种新型合成数据生成方法，旨在增强数据稀缺场景下模型的泛化能力与鲁棒性。所提出方法的核心思想是利用同类系统的知识迁移。具体而言，通过预训练的元模型生成合成数据，该模型描述了待研究系统所属的广义系统类别。训练数据具有双重作用：其一，作为预训练元模型的输入以识别系统动态特性，从而预测其行为并为新输入序列生成合成输出序列；其二，与合成数据共同定义用于模型估计的损失函数。通过验证数据集调整标量超参数，以平衡损失函数中训练数据与合成数据的相对重要性。该验证集还可用于其他目的，例如在训练过程中实现早停——这对于避免小规模训练数据集下的过拟合至关重要。数值算例展示了该方法将合成数据融入系统辨识过程的优势，验证了其有效性。