Noise-bias compensation for the unsupervised learning of constitutive laws

The Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID) framework allows the non-supervised learning of constitutive laws from full-field displacement data and global reaction forces. Nonetheless, its accuracy is adversely affected by measurement noise, resulting in biased material parameter identification due to uniform nodal weighting and mesh dependencies. To mitigate these issues, covariance-based weighting and systematic bias compensation strategies are proposed, which account for measurement uncertainties and counteract noise-induced errors. Additionally, Gaussian smoothing is introduced as a low-cost alternative to reduce noise impact by averaging nodal force residuals. These methods were evaluated using both a simplified toy model and a complex numerical test case with realistic noise levels. Results demonstrate that the proposed compensation strategies significantly enhance EUCLID's robustness and accuracy, achieving up to 93% improvement in validation metrics under high-noise conditions. Furthermore, mesh dependency issues are addressed, enabling mesh-independent learning. These advancements substantially improve the reliability of constitutive law identification in noisy experimental environments.