From LLM to FEM: Low-Rank Adaptation for Noise-Robust Structural Damage Detection.

Structural damage detection using the finite element method is inherently formulated as an inverse problem, often suffering from ill-posedness and high sensitivity to measurement noise. This study introduces a novel damage detection methodology by applying low-rank adaptation (LoRA), originally developed for fine-tuning large language models, to inverse problems in structural mechanics for the first time. The proposed approach exploits the physically inherent low-rank nature of structural damage: damage is typically localized, and the contribution of each finite element to the stiffness matrix is limited by its degrees of freedom. Accordingly, the stiffness change matrix is factorized into two low-rank matrices, reducing the number of parameters and providing implicit regularization against full-rank measurement noise. Physical consistency is ensured through sparsity and symmetry constraints. Numerical experiments on cantilever beam and L-shaped plate structures across five damage scenarios demonstrated that the proposed method achieved superior noise robustness compared with baseline methods. At a signal-to-noise ratio of 20 dB, representative of practical field conditions, LoRA achieved stiffness errors below 2%, whereas the baseline methods failed to provide reliable results. The proposed framework achieved a 100% success rate in damage zone localization (Precision@