Machine Learning-Assisted Parameter Inversion of Soil Constitutive Models: From Traditional Optimization to Neural Networks

The University of British Columbia (UBC) EOSC 2026 Annual Project explores the application of machine learning methods to determine parameters of soil constitutive models in geotechnical engineering. By combining Newton iteration inversion and neural networks, it provides new insights for geomechanical parameter identification. The project focuses on the Mohr-Coulomb constitutive model, aiming to solve the time-consuming and subjective problems of traditional parameter inversion methods and achieve automated parameter identification.

In the field of geotechnical engineering, accurately determining soil constitutive model parameters is crucial for reliable numerical analysis and engineering design. Parameters of the traditional Mohr-Coulomb model (such as bulk modulus K, shear modulus G, internal friction angle φ, and dilation angle ψ) need to be obtained through laboratory triaxial tests. However, the fitting process involves frequent manual adjustments and trial-and-error; in practical engineering, data may be incomplete or noisy, making traditional trial-and-error methods time-consuming and prone to subjective influences. Therefore, developing automated parameter inversion methods has significant engineering value.

Technical Route: Parallel adoption of physics-based numerical inversion (Newton iteration) and data-driven neural network methods. Mohr-Coulomb Model Implementation: Includes calculation of stress invariants, yield surface and plastic flow, elastoplastic stiffness matrix, and support for multiple loading conditions (drained/undrained triaxial, isotropic consolidation). Newton Iteration Inversion: Achieves stable convergence by minimizing the objective function of the difference between predicted and measured stress-strain data, combined with gradient/Hessian calculation, line search damping strategy, and physical constraints on parameters (e.g., K ≥ 1000 kPa). Neural Network Method: Learns the nonlinear mapping between parameters and stress-strain responses, which is more robust to noisy data and complex loading paths.

Typical workflow:

1. Data Preparation: Obtain laboratory triaxial test data (supports TMD/TMU formats);
2. Parameter Initialization: Set initial values for K, G, φ, ψ;
3. Inversion Calculation: Run Newton iteration to automatically adjust parameters;
4. Result Verification: Output optimal parameters, convergence history, and comparison charts between predicted and measured curves.

Technical highlights:

• Migration from MATLAB to Python: Porting classic algorithms to the Python ecosystem for easier integration with machine learning frameworks;
• Manual Numerical Differentiation: No automatic differentiation framework used; gradients/Hessians are calculated via numerical differentiation to fully control algorithm details;
• Modular Design: Functions are encapsulated as independent modules for easy reuse and expansion;
• Binder Integration: Supports running Notebooks in the browser, lowering the barrier to use.

Limitations and future directions:

• Model Simplification: Only supports the Mohr-Coulomb model; needs to be extended to complex hardening models (e.g., Cam-Clay);
• Data Requirements: Newton iteration requires reasonable initial parameters; neural networks need large amounts of labeled data;
• Computational Efficiency: Numerical differentiation is costly in high-dimensional parameter spaces; automatic differentiation/adjoint methods can be introduced;
• Insufficient Verification: Some visualization functions are to be developed; additional verification cases and documentation need to be supplemented.

Practical Implications: Combining traditional mechanical models with machine learning retains physical interpretability while improving efficiency and robustness; automated tools reduce post-test processing workload and enhance parameter objectivity, especially suitable for large datasets or sensitivity analysis; lays the foundation for the development of intelligent geotechnical engineering tools. Conclusion: Although the project is still under development, the approach of combining physical inversion and machine learning is valuable for reference. Once improved, it is expected to become a powerful tool for geotechnical engineers and researchers, promoting the field towards intelligent and efficient development.