Bayesian-Optimized Physics-Informed Deep Autoencoders for Efficient Calibration of Geotechnical Constitutive Models: A NorSand Case Study

Recent advancements in deep learning have revolutionized constitutive model calibration in geotechnical engineering by automatically identifying complex patterns in high-dimensional data, enhancing accuracy, and reducing reliance on subjective human biases. This paper presents a novel approach that employs physics-informed deep autoencoders to determine the optimal number of triaxial tests required for calibrating the NorSand constitutive model. The proposed methodology integrates machine learning techniques with physical principles embedded in the data, enabling efficient extraction of relevant features from experimental results while ensuring consistency with the governing physics of soil mechanics. Also, a Bayesian optimization procedure is carried out to find the best balance between the reconstruction and the physics-based loss terms during training. A comprehensive analysis is conducted to explore the relationship between the number and types of triaxial tests and the fidelity of the model predictions using a data set generated from synthetic simulations. Such analysis demonstrated that physics-informed autoencoders can accurately estimate constitutive parameters using as few as one drained and one undrained triaxial tests without statistically compromising accuracy. This work advances geotechnical practice by providing a robust framework for optimizing experimental design in soil testing, leading to more reliable and cost-effective engineering solutions for addressing complex soil behaviors, such as liquefaction.