Discovering Partially Known Ordinary Differential Equations: a Case Study on the Chemical Kinetics of Cellulose Degradation

2025-04-04

AI Summary

Modeling aging of mineral-oil-impregnated cellulose insulation in power transformers faces challenges due to scarcity of degree-of-polymerization (DP) data and insufficient physical priors—both structural and parametric—in conventional ordinary differential equation (ODE) models (e.g., Ekenstam or Emsley models). Method: This work integrates physics-informed and data-driven approaches, introducing for the first time a synergistic framework combining physics-informed neural networks (PINNs) with symbolic regression for dynamical modeling. We propose a novel time-varying, temperature-dependent decay rate constant grounded in the Arrhenius principle, enabling joint discovery of ODE structure and parameters. Contribution/Results: The method successfully recovers the functional form and unknown parameters of the key ODE in the Emsley model. Validated on both synthetic and real-world DP datasets, the model achieves significantly improved prediction accuracy and mechanistic interpretability, establishing a new paradigm for insulation aging modeling under small-data regimes.

Technology Category

• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

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.

Problem

• Discover ODEs for cellulose degradation in power transformers
• Estimate unknown parameters in Arrhenius-based aging models
• Identify functional forms of degradation ODEs using PINNs

Innovation

• Physics-Informed Neural Networks model degradation
• Symbolic regression recovers ODEs governing aging
• Modified Arrhenius equation tracks time-dependent rates