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Original Research Open Access

Physics-Informed Neural Networks for Steel Beam Deflection Analysis: Methodology and Applications

  • 1Professor, Civil Engineering Department, K.N. Toosi University of Technology, Tehran, Iran
  • 2Independent Researcher in Physics?Informed Neural Networks and Scientific Machine Learning, Tehran, Iran
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Corresponding Author

H Mirzabozorg, mirzabozorg@kntu.ac.ir

Received Date: October 07, 2025

Accepted Date: November 11, 2025

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

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