Physics-informed polynomial chaos expansions for geometric uncertainties

Collecting large experimental datasets that accurately depict the behavior of complex systems under uncertainty poses a significant challenge.In such scenarios, surrogate models such as Polynomial Chaos Expansion (PCE) benefit from incorporating problem-specific physical information.This integration facilitates the reduction of the necessary training data, thereby enabling efficient estimation of the system's response.Nevertheless, when uncertainties arise from geometric variations, traditional Finite Element Analysis (FEA) methods are limited in generating training datasets for PCE coefficient estimation due to mesh dependency and potential inaccuracies in geometry approximation.To address these limitations, this study explores a novel methodology that uses Isogeometric Analysis (IGA) to generate physical insights for systems with geometric uncertainties.These insights are then employed to construct a Physics-informed PCE (PC 2 ), which directly integrates IGA sensitivities to embed constraints, such as boundary conditions and system behavior, into the surrogate model.The corresponding sensitivities are computed as a by-product of the analysis using a variational approach.A case study demonstrates the efficacy of the method in predicting complex responses, such as stress triaxiality, while maintaining a balance between computational cost and accuracy.Furthermore, the results demonstrate a 40% reduction in mean squared error (MSE) when employing the proposed IGA-sensitivity-based PC 2 in contrast to sparse Least Angle Regression (LAR) PCE.This suggests that the proposed strategy can provide more accurate estimates than traditional PCE approaches applied to geometric uncertainties, highlighting its potential for broader uncertainty quantification and surrogate modeling applications.