GRADIENT-DRIVEN BAYESIAN MODEL UPDATING FRAMEWORK BASED ON DIFFERENTIABLE FINITE-ELEMENT METHOD

Bayesian model updating has been widely applied for material parameter inversion and uncertainty quantification in aerospace, civil, and hydraulic engineering. However, gradient information was prohibitively expensive to obtain from conventional finite-element method. As a result, the reliance on gradient-free Bayesian methods was necessitated. The inference efficiency and convergence of these methods were known to degrade substantially in complex problems when compared with gradient-driven alternatives. To address this limitation, a Bayesian model updating framework based on the differentiable finite-element method was developed. A hybrid automatic-differentiation–adjoint strategy was adopted to obtain gradients, offering low memory consumption and high generality. This strategy enabled the differentiable finite-element method to compute gradients of structural responses with respect to model parameters efficiently alongside forward solutions. These exact gradients were supplied to the No-U-Turn Sampler (NUTS), by which an integrated coupling between gradient-driven Bayesian inference and finite-element forward modelling was established. Likelihood functions were constructed using displacement and internal force responses, respectively. The proposed framework was validated through two classical mechanics examples, where high accuracy in parameter inference and strong robustness were observed. Both the sampling efficiency and the number of parameters that could be handled simultaneously were found to substantially exceed those of gradient-free methods. Through the deep integration of gradient-driven inference with the differentiable finite-element method, the proposed framework substantially improved the efficiency and convergence of model updating in complex problems, while preserving the high-fidelity solution capability of the finite-element method.