Differentiable Machine Learning in Geotechnical Engineering: A Case Study of Bearing Capacity Prediction of Shallow Foundation on Cohesionless Soils

Machine learning (ML) has emerged as a powerful tool across various scientific and engineering fields. However, traditional ML models often function as black-box systems, offering limited interpretability and struggling with generalization. To address these limitations, this study introduces a novel differentiable modelling neural network (DMNN) for predicting bearing capacity of shallow foundations on cohesionless soil. By leveraging differentiable architectures, DMNN combines the flexibility and scalability of data-driven learning with the interpretability of physical models. In this study, a simulated dataset was generated based on Meyerhof’s theories. The dataset was divided into non-overlapping clusters to assess model’s generalization. Random noise was added to evaluate the model’s robustness. The results indicated that the proposed DMNN performed consistently well on different testing clusters with R2 of 0.99, showing a good generalization. It also outperformed pure data-driven NN with R2 of 0.98 with noisy training data. Further evaluation using a compiled database with actual cases also revealed that DMNN generally outperformed pure data-driven NN in cases with a small training data size. The findings highlight the capability of differentiable ML to bridge pure data-driven models and physical knowledge, showing its significant potential for practical applications and further research innovation in geotechnical engineering.