Previous research in the scientific field has utilized statistical empirical models and machine learning to address fitting challenges. While empirical models have the advantage of numerical generalization, they often sacrifice accuracy. However, conventional machine learning methods can achieve high precision but may lack the desired generalization. The article introduces a Regression-based Physics-Informed Neural Networks (Reg-PINNs), which embeds physics-inspired empirical models into the neural network's loss function, thereby combining the benefits of generalization and high accuracy. The study validates the proposed method using the magnetopause boundary location as the target and explores the feasibility of methods including Shue et al. [1998], a data overfitting model, a fully-connected networks, Reg-PINNs with Shue's model, and Reg-PINNs with the overfitting model. Compared to Shue's model, this technique achieves approximately a 30% reduction in RMSE, presenting a proof-of-concept improved solution for the scientific community.

翻译：先前科学研究中常采用统计经验模型与机器学习方法应对拟合挑战。经验模型虽具备数值泛化优势，但往往以牺牲精度为代价；而传统机器学习方法虽能实现高精度，却可能缺乏理想的泛化能力。本文提出一种基于回归的物理信息神经网络（Reg-PINNs），将具有物理启发性的经验模型嵌入神经网络的损失函数，从而融合泛化性与高精度优势。研究以磁层顶边界定位为目标验证所提方法，系统探讨了Shue等人[1998]模型、数据过拟合模型、全连接网络、结合Shue模型的Reg-PINNs以及结合过拟合模型的Reg-PINNs等方法的可行性。相较于Shue模型，该技术实现了约30%的均方根误差降低，为科学界提供了一种概念验证性的改进解决方案。