Learning Material-Geometry-Aware Fourier Neural Operator for Stress–Strain Prediction and Parameter Inversion

Accurately predicting the internal stress–strain distribution and inversely identifying unknown material properties are two important long-standing challenges in solid mechanics. Traditional high-fidelity numerical methods and existing deep learning approaches have achieved notable progress and have been widely applied. However, traditional numerical methods are computationally expensive, while existing deep learning approaches struggle with complex material properties and geometries. In this paper, we propose a novel Material-Geometry-Aware Fourier Neural Operator (MGA-FNO) to address these issues: it integrates a material-aware encoder for complex properties, a geometry-aware module for Cubic Bézier parameterized irregular defects, and fuses features into a Neural Operator (FNO) backbone for mesh-independent modeling. For stress–strain distribution prediction, MGA-FNO achieves [Formula: see text] (strain field, MAPE = 1.03%) and [Formula: see text] (stress field, MAPE = 0.129%), taking only 1.1 ms/sample; For inverse parameter identification, single-parameter inversion (e.g., yield strength [Formula: see text], ultimate tensile strength [Formula: see text]) reaches MAPE averaging 0.2%; multi-parameter inversion (Young’s modulus [Formula: see text]) maintains MAPE about 3%. It completes inversion in 6.75 s/sample. Mesh-independence and out-of-distribution tests further confirm its adaptability. MGA-FNO provides an efficient and scalable framework for computational mechanics, structural assessment, and non-destructive testing.