Neural network models have shown outstanding performance and successful resolutions to complex problems in various fields. However, the majority of these models are viewed as black-box, requiring a significant amount of data for development. Consequently, in situations with limited data, constructing appropriate models becomes challenging due to the lack of transparency and scarcity of data. To tackle these challenges, this study suggests the implementation of a grey-informed neural network (GINN). The GINN ensures that the output of the neural network follows the differential equation model of the grey system, improving interpretability. Moreover, incorporating prior knowledge from grey system theory enables traditional neural networks to effectively handle small data samples. Our proposed model has been observed to uncover underlying patterns in the real world and produce reliable forecasts based on empirical data.

翻译：神经网络模型在多个领域展现出卓越性能，并能成功解决复杂问题。然而，这类模型大多被视为黑箱，需要大量数据支持开发。因此，在数据有限的场景中，由于缺乏透明性和数据稀缺性，构建合适的模型变得充满挑战。为应对这些问题，本研究提出一种灰色信息神经网络（GINN）。GINN确保神经网络的输出遵循灰色系统的微分方程模型，从而提升可解释性。此外，融合灰色系统理论的先验知识，使传统神经网络能有效处理小样本数据。实验表明，我们所提出的模型能够揭示现实世界中的潜在规律，并基于经验数据生成可靠的预测结果。