LLM-PDPC-SR: physics-informed equation discovery of power device physical characteristics

Accurate lifetime prediction of power devices (e.g., insulated gate bipolar transistors (IGBTs)) is crucial for ensuring the safety of power electronic systems; however, existing methods often struggle to balance model accuracy with physical interpretability. To address this challenge, this study proposes a symbolic regression (SR) method guided by power device physical characteristics (PDPC) via large language models (LLM), termed LLM-PDPC-SR. Inspired by existing LLM-SR methods, LLM-PDPC-SR aims to automatically discover high-precision, interpretable IGBT physical characteristics (PC) mathematical equations linking easily measurable electrical parameters with IGBT PC (e.g., lifetime). Specifically, we encode key IGBT failure mechanisms into constraint information through customized prompts that incorporate PDPC and example-assisted mathematical structures, guiding the LLM toward a more effective search in the symbolic space. LLM-PDPC-SR consists of PDPC equation hypothesis generation, equation factor optimization, and PDPC-enhanced multi-island experience management. Our LLM-PDPC-SR-discovered equation validated on an IGBT lifetime equation discovery task on a publicly available NASA dataset significantly outperforms existing methods in accuracy (3.95×10−4 vs physics-based 3.21×10−1 and SR 5.70×10−4 in normalized mean squared error (NMSE)). Additionally, its structural simplicity and physically meaningful terms incorporate high-temperature and multi-physics coupling effects, which offers new insights into IGBT degradation and demonstrates potential in predictive maintenance.