Journal of Visual Computing logo

Articles

Vol. 1 No. 4 (2026)

Sparse Symbolic Surrogates for Path-Dependent Clay Constitutive Response

Submitted
August 1, 2026
Published
August 15, 2026

Abstract

Constitutive modeling of clay remains one of the most challenging areas in computational geomechanics due to the highly nonlinear and path-dependent nature of soil deformation. Traditional elastoplastic and viscoplastic models require complex numerical integration schemes that are computationally expensive and prone to convergence issues in large-scale finite element simulations. While deep learning models such as neural networks have emerged as popular surrogate models to bypass these computational bottlenecks, their black-box nature obscures physical interpretability and limits their reliable extrapolation to unseen stress paths. This paper introduces a novel framework utilizing sparse symbolic regression to discover interpretable, algebraic surrogate models for the path-dependent constitutive response of clay. By leveraging sparse identification algorithms, we extract parsimonious differential equations that accurately map strain increments to stress increments while maintaining internal state variables. The methodology generates an extensive synthetic dataset using advanced bounding surface plasticity models to train the symbolic surrogate. Optimization is performed through a sequentially thresholded least-squares approach with sparsity-promoting regularization. The resulting symbolic surrogates not only drastically reduce computational evaluation times but also provide explicit mathematical expressions that reflect underlying physical mechanisms such as plastic hardening and volumetric dilation. Comparative analyses demonstrate that the proposed sparse symbolic surrogates rival the accuracy of deep recurrent neural networks while offering superior generalization capabilities and strictly enforcing physical constraints.

References

  1. 1. Zhang, J., Peng, H., Sun, L., Wu, G., Liu, C., & Yu, Z. (2025, August). Unsupervised graph clustering with deep structural entropy. In Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 2 (pp. 3752-3763).
  2. 2. Li, H., Duan, M., Yang, X., Wang, R., & Ouyang, Z. (2025). Modified CPTU parameters and SBTn chart for predicting shear behavior of organic soils at large strains. Engineering Geology, 108273.
  3. 3. Yu, K., Ran, Y., Shi, J., Duan, M., & Ouyang, Z. (2025). Physical property of MICP-treated calcareous sand under seawater conditions by CPTU. Biogeotechnics, 3(1), 100131.
  4. 4. Ouyang, Z., Feng, H., Yang, J., Gu, X., Shi, J., & Li, H. (2026). Interpretation of soil deformation characteristics based on in-situ test: A comprehensive review. Ocean Engineering, 352, 124508.
  5. 5. Ran, Y., Ouyang, Z., Zhou, J., Hu, Z., & Liao, R. (2026). Micro-macro evolution of EICP-treated sand characterized by polarization measurement. Acta Geotechnica, 1-20.
  6. 6. Li, Y. Z., Zhang, J. P., Chen, Z. Y., Wang, H. C., Zhang, K. X., Hu, S. S., ... & Dudley, M. (2026, September). Growth and Characterization of High-Quality Thick Epitaxial 4H-SiC Wafers for High Voltage Devices. In Defect and Diffusion Forum (Vol. 452, pp. 79-85). Trans Tech Publications Ltd.
  7. 7. Li, X., Wang, P., Li, G., & Zhang, Y. (2023). Design of a novel self-test-on-chip interface ASIC for capacitive accelerometers. IEEE Transactions on Circuits and Systems I: Regular Papers, 70(7), 2834-2843.
  8. 8. Xiong, S., Chen, T., Rupendra, A., Clement, C., Gasparri, E., & Lucchi, E. (2026). Embodied Carbon of Progressive Timber Integration in a 47-Storey Tropical High-Rise: A Singapore Public Housing Case Study. Building and Environment, 114910.
  9. 9. Yu, A., Huang, Y., Li, S., Wang, Z., & Xia, L. (2023). All fiber optic current sensor based on phase-shift fiber loop ringdown structure. Optics Letters, 48(11), 2925-2928.
  10. 10. Zhang, S., & Yan, W. (2025). In-trainNet: A Two-Step Data-Driven Framework for Enhancing Railway In-Train Forces Monitoring. Advanced Engineering Informatics, 65, 103352.
  11. 11. Luan, S., Wang, P., Zhang, L., He, Y., Huang, X., Jian, G.,... & Fu, Z. (2023). Atmospherically hydrothermal assisted solid-state reaction synthesis of ultrafine BaTiO3 powder with high tetragonality. Journal of Electroceramics, 50 (4), 97-111.
  12. 12. Wang, Y. Y., Lou, M., Wang, Y., Wu, W. G., & Yang, F. (2022). Stochastic failure analysis of reinforced thermoplastic pipes under axial loading and internal pressure. China Ocean Engineering, 36(4), 614-628.
  13. 13. Wang, S., Huang, S., Qiu, T., Yang, J., Zhong, J., & Hu, Q. (2020). Analytical study of the permeability of a foam-conditioned soil. International Journal of Geomechanics, 20(8), 06020019.
  14. 14. Zhao, R., Tang, J., Zeng, W., Chen, Z., & Zhao, X. (2024, October). Zero-shot knowledge graph question generation via multi-agent llms and small models synthesis. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management (pp. 3341-3351).
  15. 15. Li, Q., Ye, Q., Zhang, N., Zhang, W., & Hu, F. (2025). Digital-twin-enabled industrial IoT: Vision, framework, and future directions. IEEE Wireless Communications, 32(6), 173-181.
  16. 16. Li, S. (2025). Momentum, volume and investor sentiment study for us technology sector stocks—A hidden markov model based principal component analysis. PloS one, 20(9), e0331658.
  17. 17. Li, X., Wang, P., Li, G., Ni, L., & Zhang, Y. (2023). Design of interface circuits and lightweight PUF for TMR sensors. IEEE Sensors Journal, 23(11), 11754-11761.
  18. 18. Liang, R., Xu, S., Xie, C., Chen, J., Ren, F., Yang, S., & Yabe, T. (2026). Abstain Mask Retain Core: Time Series Prediction by Adaptive Masking Loss with Representation Consistency. Advances in Neural Information Processing Systems, 38, 99445-99471.
  19. 19. Li, S. (2024). Machine Learning in Credit Risk Forecasting — — A Survey on Credit Risk Exposure. Accounting and Finance Research, 13(2), 107-107.
  20. 20. Sha, L., Wang, Y., Meng, P., Deng, Y., Chen, T., Zhang, X., ... & Xu, Q. (2025). Pharmacological inhibition of PSPH reduces serine levels and epileptic seizures. Nature Chemical Biology, 21(11), 1742-1753.
  21. 21. Ghosh, R., Jia, X., Yin, L., Lin, C., Jin, Z., & Kumar, V. (2022, November). Clustering augmented self-supervised learning: an application to land cover mapping. In Proceedings of the 30th International Conference on Advances in Geographic Information Systems (pp. 1-10).
  22. 22. Zhang, Y., Huang, Z., Zhao, M., Zhang, C., Lu, Y., Ji, Y., ... & Zeng, A. (2025). Learning unbiased cluster descriptors for interpretable imbalanced concept drift detection. IEEE Transactions on Emerging Topics in Computational Intelligence.
  23. 23. Tan, Z., Luo, X., Liu, Y., & Zhang, Y. (2026, March). Mask the redundancy: Evolving masking representation learning for multivariate time-series clustering. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 40, No. 30, pp. 25787-25795).
  24. 24. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B, 58(1), 267–288.