Abstract
This paper presents an enhanced Physics-Informed Neural Network (PINN) methodology for structural beam deflection analysis, introducing three methodological contributions that address computational challenges in mechanics: a penalty-based boundary condition enforcement framework, a time-decaying adaptive boundary loss weight, and a regularized representation of concentrated loads via Gaussian approximation. The proposed approaches are validated on cantilever, fully-restrained, and mid-span point loaded beams, demonstrating both accuracy and training efficiency. The adaptive weighting reduced required training iterations by approximately 37% compared to static equal-weight baselines, achieving training losses on the order of 10−10 and relative L2 errors as low as 0.056% for concentrated load cases.
Keywords
Physics-informed neural networks, Steel beam deflection, Structural mechanics, Gaussian regularization, Adaptive weighting