用神经网络从老化数据中反推纤维素降解的微分方程，揭示温度影响下的动态退化机制。
Discovering Partially Known Ordinary Differential Equations: a Case Study on the Chemical Kinetics of Cellulose Degradation
- 结合物理约束神经网络与符号回归，从真实和合成数据中恢复退化方程
- 发现阿伦尼乌斯参数随时间变化，修正了原有模型中的速率常数假设
- 适用于电力设备绝缘老化建模，尤其适合数据稀缺场景
聚合度（DP）是评估聚合物绝缘系统老化的重要指标，如电力设备中的纤维素绝缘。主要降解机制包括水解、热解和氧化，共同导致DP下降。然而，此类问题的数据通常稀缺。本研究基于电力变压器中纤维素在矿物油中的老化数据，建立常微分方程（ODE）模型描述绝缘老化过程。采用物理信息神经网络（PINNs）和符号回归方法，恢复退化系统的控制方程。针对合成数据和真实DP值，应用PINNs识别描述纤维素污染含量与温度相关老化过程的埃肯斯塔姆ODE中阿伦尼乌斯方程的未知参数。对埃姆斯利系统进行改进，使阿伦尼乌斯表达式中的速率常数随时间衰减。通过PINNs与符号回归，恢复该系统中一个ODE的函数形式，并识别出未知参数。
原文摘要 · Abstract (English)
The degree of polymerization (DP) is one of the methods for estimating the aging of the polymer based insulation systems, such as cellulose insulation in power components. The main degradation mechanisms in polymers are hydrolysis, pyrolysis, and oxidation. These mechanisms combined cause a reduction of the DP. However, the data availability for these types of problems is usually scarce. This study analyzes insulation aging using cellulose degradation data from power transformers. The aging problem for the cellulose immersed in mineral oil inside power transformers is modeled with ordinary differential equations (ODEs). We recover the governing equations of the degradation system using Physics-Informed Neural Networks (PINNs) and symbolic regression. We apply PINNs to discover the Arrhenius equation's unknown parameters in the Ekenstam ODE describing cellulose contamination content and the material aging process related to temperature for synthetic data and real DP values. A modification of the Ekenstam ODE is given by Emsley's system of ODEs, where the rate constant expressed by the Arrhenius equation decreases in time with the new formulation. We use PINNs and symbolic regression to recover the functional form of one of the ODEs of the system and to identify an unknown parameter.
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