I-PINN: Physics-Informed Neural Network Fused with Image Information, Opening a New Paradigm for Solving Inverse Problems in Solid Mechanics

I-PINN (Physics-Informed Neural Network Fused with Image Information) framework combines image matching with physical constraints, and through a two-stage inverse problem solving process, achieves high-precision prediction from speckle images to material parameter identification. This framework provides a new paradigm for solving inverse problems in solid mechanics, with its core lying in the deep integration of Digital Image Correlation (DIC) technology and physics-informed neural networks to build a unified optimization framework.

In the field of solid mechanics, solving inverse problems is a core challenge in engineering practice. The traditional Finite Element Method (FEM) has high accuracy but requires prior knowledge of material parameters and is computationally expensive; Digital Image Correlation (DIC) technology can obtain full-field displacement data, but how to effectively combine physical laws to achieve automatic material parameter identification is a focus of the academic community. I-PINN was born in this context, fusing PINN with image information to solve inverse problems in solid mechanics.

I-PINN adopts a two-stage inverse problem solving strategy: the first stage focuses on image matching, learning the deformation mapping from the reference to the target image; the second stage introduces physical constraints (equilibrium equations, boundary conditions, energy consistency, etc.) to refine the results. The framework uses a modular design, with core modules including framework.py (training process), cases.py (case definition), model.py/materials.py (network and material parameters), and constraints.py (loss functions), supporting multi-constraint collaborative optimization (image deformation, displacement/stress boundary conditions, internal equilibrium, energy consistency, etc.).

The single-hole plate benchmark test case simulates the horizontal stretching scenario of a rectangular plate with a central circular hole. Input data includes speckle images, finite element reference fields, etc. The framework supports fixed material parameters and inverse mode (parameter identification): in inverse mode, the predicted Young's modulus is 2.9971 (error -0.29%), and Poisson's ratio is 0.3221 (error +0.21%). Quantitative evaluation shows that the accuracy of displacement field, strain field, and stress field is highly consistent with the finite element reference solution (e.g., root mean square error in the u direction is 0.02398).

The experiment reproduction environment is based on Python3.11, PyTorch2.7.0, etc. To install dependencies, run pip install -r requirements.txt. Quick start: basic mode python code/run_single_hole_inverse.py --case-dir example_case; add --invert-material for inverse problem mode. Result evaluation and visualization can generate comparison figures through the evaluate_single_hole.py and export_comparison_figures.py scripts.

The innovations of I-PINN include: 1. Deep fusion of image and physics, deriving strain fields, stress fields, and material parameters from images; 2. Scalable framework design, easily extending to new scenarios through case objects; 3. High-precision material identification (error <0.3%); 4. Complete experiment reproduction package (code, sample data, reference results, etc.), lowering the threshold for reuse.

I-PINN has broad application prospects in engineering fields: material characterization (automatic parameter identification), structural health monitoring (detecting deformation and damage), reverse engineering (inferring material distribution or boundary conditions), and experimental mechanics research (improving DIC measurement accuracy).

I-PINN is an important progress of PINN in inverse problems of solid mechanics, achieving high-precision prediction from speckle images to mechanical fields and material parameters. Its modular design makes it an open-source framework, and it is expected to become a standard tool for experimental solid mechanics in the future. It is suitable for researchers in computational mechanics, experimental mechanics, or machine learning applications to try.