On the synthesis of the measurements and structural models using statistical finite element method

In this paper, we present a statistical finite element method (statFEM) for the synthesis of measurement data and computational models of architected metamaterials under material and model uncertainty. The proposed framework combines a probabilistic forward model with Bayesian inference to update displacement fields using sparse, noisy observations. Synthetic measurements are generated using a high-fidelity Timoshenko beam model, while inference is performed with a reduced Euler–Bernoulli model, thereby introducing controlled model discrepancy. Material uncertainty is modelled as a Gaussian random field defined over the connectivity graph of the lattice, with a covariance structure derived from a discretised stochastic partial differential equation (SPDE). This formulation yields sparse precision matrices that enable efficient Bayesian updating for large-scale lattice systems. Numerical studies on body-centred cubic (BCC) and octet lattice structures demonstrate that the proposed approach can recover accurate solution fields from limited measurements, reduce predictive uncertainty, and identify regions most affected by model mismatch and connectivity defects. Our results show that the SPDE-based statFEM framework provides a computationally tractable and statistically rigorous approach for fusing data and models of metamaterials. It offers a promising extension to uncertainty-aware digital twins of architected materials and structures. • Bayesian framework integrates sparse measurements with FE models of lattices. • Bayesian framework combines sparse, noisy measurements with FE models of lattice structures. • Material uncertainty is propagated to displacements using a probabilistic, connectivity-based covariance model. • SPDE-based formulation enables scalable statistical FE inference for large lattice systems. • Results provide accurate displacement updates, uncertainty reduction, and support uncertainty-aware digital twins of metamaterials.