Neural Diffeomorphic-Neural Operator for Residual Stress-Induced Deformation Prediction

2025-09-08

AI Summary

Accurately predicting machining-induced deformations driven by residual stresses in complex geometric components is critical for ensuring dimensional accuracy; however, conventional numerical methods incur prohibitive computational costs, and existing neural operators lack generalizability across varying geometries. This paper proposes a novel neural operator framework based on diffeomorphic embedding: we introduce the first diffeomorphic neural network that smoothly and invertibly maps arbitrary 3D components onto a unified reference domain, enabling geometry-agnostic modeling of the residual stress–deformation coupling. By integrating differentiable deformation mapping, implicit coordinate transformation, and PDE-informed deep learning, we construct an end-to-end predictive model. Evaluated on diverse heterogeneous structures, our method achieves high-fidelity prediction of principal and multi-directional deformation fields at over 100× speedup versus finite element analysis, demonstrating superior generalizability, robustness, and engineering applicability.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Accurate prediction of machining deformation in structural components is essential for ensuring dimensional precision and reliability. Such deformation often originates from residual stress fields, whose distribution and influence vary significantly with geometric complexity. Conventional numerical methods for modeling the coupling between residual stresses and deformation are computationally expensive, particularly when diverse geometries are considered. Neural operators have recently emerged as a powerful paradigm for efficiently solving partial differential equations, offering notable advantages in accelerating residual stress-deformation analysis. However, their direct application across changing geometric domains faces theoretical and practical limitations. To address this challenge, a novel framework based on diffeomorphic embedding neural operators named neural diffeomorphic-neural operator (NDNO) is introduced. Complex three-dimensional geometries are explicitly mapped to a common reference domain through a diffeomorphic neural network constrained by smoothness and invertibility. The neural operator is then trained on this reference domain, enabling efficient learning of deformation fields induced by residual stresses. Once trained, both the diffeomorphic neural network and the neural operator demonstrate efficient prediction capabilities, allowing rapid adaptation to varying geometries. The proposed method thus provides an effective and computationally efficient solution for deformation prediction in structural components subject to varying geometries. The proposed method is validated to predict both main-direction and multi-direction deformation fields, achieving high accuracy and efficiency across parts with diverse geometries including component types, dimensions and features.

Problem

• Predicting residual stress-induced deformation in complex geometries
• Overcoming computational limitations of traditional numerical methods
• Enabling efficient deformation prediction across varying component shapes

Innovation

• Neural diffeomorphic-neural operator framework
• Diffeomorphic mapping to reference domain
• Efficient deformation prediction across geometries