Deformable Fabric State Estimation for Composite Forming via Physics-Informed Data Assimilation

Accurate state estimation of deformable materials remains challenging due to model uncertainty, contact interactions, and limited observational data. We present a physics-informed neural network for state estimation in fabric-forming processes. Carbon-fibre fabric is modelled as a mesh of damped springs with frictional contact against a rigid tool over continuous-time. The approach is experimentally validated on a hemispherical tool and a fabric with a 15-by-15 grid of tracked markers by 3D vision. Sparse marker observations are assimilated during training, and performance is evaluated on held-out marker locations. In a ten-fold cross validation, the approach reduces prediction errors at unseen locations by more than 80% compared to the physics baseline. Furthermore, we show how accuracy increases with increasing assimilation data and how severe sparsity is handled. Our results demonstrate that physics-informed learning with data assimilation can reconstruct full-field deformable-system states from limited observations, providing a pathway toward digital twins and decision-making for composite manufacturing processes.