用神经微分方程求解白矮星密度分布，验证了AI在天体物理中的预测能力。
A comparative study of NeuralODE and Universal ODE approaches to solving Chandrasekhar White Dwarf equation
- 采用神经微分方程与通用微分方程建模白矮星结构方程。
- 发现两类模型在特定时间后均出现预测失效，提出预报崩溃点概念。
- 揭示网络结构与优化器对模型性能的关键影响，适合天文建模研究者参考。
本研究将科学机器学习的两大支柱——神经微分方程（Neural ODEs）和通用微分方程（UDEs）应用于钱德拉塞卡白矮星方程（CWDE）。该方程是理解恒星演化周期的基础，描述白矮星密度与中心距离的关系。尽管科学机器学习框架日益发展，但其在基于微分方程的天体物理问题上的系统性应用仍较少。通过在Julia语言中进行稳健建模，我们证明了神经微分方程和通用微分方程均可有效用于预测和预报。更重要的是，我们提出了预报崩溃点——即两类模型同时失效的时间点。通过系统的超参数优化测试，揭示了最优神经网络架构、激活函数与优化器组合。本研究为科学机器学习在多类科学领域预报任务中的应用开辟了新路径。
原文摘要 · Abstract (English)
In this study, we apply two pillars of Scientific Machine Learning: Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs) to the Chandrasekhar White Dwarf Equation (CWDE). The CWDE is fundamental for understanding the life cycle of a star, and describes the relationship between the density of the white dwarf and its distance from the center. Despite the rise in Scientific Machine Learning frameworks, very less attention has been paid to the systematic applications of the above SciML pillars on astronomy based ODEs. Through robust modeling in the Julia programming language, we show that both Neural ODEs and UDEs can be used effectively for both prediction as well as forecasting of the CWDE. More importantly, we introduce the forecasting breakdown point - the time at which forecasting fails for both Neural ODEs and UDEs. Through a robust hyperparameter optimization testing, we provide insights on the neural network architecture, activation functions and optimizers which provide the best results. This study provides opens a door to investigate the applicability of Scientific Machine Learning frameworks in forecasting tasks for a wide range of scientific domains.
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