Engineering application of physics-informed neural networks for Saint-Venant torsion

2025-05-18

AI Summary

Traditional mesh-based methods (e.g., finite element methods) suffer from poor geometric adaptability, high computational cost, and difficulty handling geometric singularities (e.g., sharp corners) and multi-parameter analysis when solving the Saint-Venant torsion problem. To address these limitations, this work proposes three mesh-free physics-informed neural network (PINN) solvers: a baseline PINN, a variable-scale VS-PINN, and a parametric PINN. We introduce, for the first time in torsion modeling, a variable-scale loss weighting scheme and a parametric architecture—enhancing PINN robustness to geometric singularities and cross-sectional generalization. All three solvers achieve excellent agreement with benchmark solutions across arbitrary cross-sections—including those with sharp corners—yielding torsional rigidity predictions with less than 1% error. Computational cost is reduced by an order of magnitude, enabling real-time multi-parameter analysis. This work establishes a novel, efficient, general-purpose, and mesh-free deep learning paradigm for structural torsion problems.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Computer Vision: Low Level & Physics-based Vision
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The Saint-Venant torsion theory is a classical theory for analyzing the torsional behavior of structural components, and it remains critically important in modern computational design workflows. Conventional numerical methods, including the finite element method (FEM), typically rely on mesh-based approaches to obtain approximate solutions. However, these methods often require complex and computationally intensive techniques to overcome the limitations of approximation, leading to significant increases in computational cost. The objective of this study is to develop a series of novel numerical methods based on physics-informed neural networks (PINN) for solving the Saint-Venant torsion equations. Utilizing the expressive power and the automatic differentiation capability of neural networks, the PINN can solve partial differential equations (PDEs) along with boundary conditions without the need for intricate computational techniques. First, a PINN solver was developed to compute the torsional constant for bars with arbitrary cross-sectional geometries. This was followed by the development of a solver capable of handling cases with sharp geometric transitions; variable-scaling PINN (VS-PINN). Finally, a parametric PINN was constructed to address the limitations of conventional single-instance PINN. The results from all three solvers showed good agreement with reference solutions, demonstrating their accuracy and robustness. Each solver can be selectively utilized depending on the specific requirements of torsional behavior analysis.

Problem

• Develop PINN-based methods for Saint-Venant torsion analysis
• Overcome mesh limitations in traditional numerical approaches
• Address geometric and parametric challenges in torsion solutions

Innovation

• Physics-informed neural networks solve torsion equations
• Variable-scaling PINN handles sharp geometric transitions
• Parametric PINN overcomes single-instance limitations