A differentiable energy minimization framework for massive parallel analysis of laterally loaded piles

Current design objectives of laterally loaded piles are increasingly shifting from deterministic calculations to reliability-based analysis to consider various uncertainties, which requires extensive sample evaluations and brings great computational challenges to conventional analytical frameworks. This study proposes a Differentiable Energy Minimization framework for Pile Analysis (DEM-PA), which enables the rapid parallel analysis of a massive number of samples without sacrificing accuracy. Based on the principle of minimum total potential energy, DEM-PA discretizes the pile and directly treats the nodal degrees of freedom (DOFs) as optimizable variables, minimizing the global energy functional via backpropagation and optimization algorithms. By employing localized Gaussian quadrature, the framework effectively decouples the simulation of pile deformation and soil resistance. This allows it to accurately capture complex local soil fluctuations with minimal active DOFs. By structuring all computations into standardized tensor formats, DEM-PA leverages Graphics Processing Unit (GPU) parallelization for the simultaneous evaluation of massive samples. Validations confirm its high accuracy and robustness in nonlinear, spatially variable and layered soils. Applications demonstrate its capability to process large samples (100,000) within seconds, offering a highly efficient tool for reliability-based design.