Physics-based pruning neural network for global sensitivity analysis

Abstract

Global sensitivity analysis (GSA) is essential to quantify the variation of model response sourced from the uncertainty of input variables over the entire design space. To address challenges in high-dimensional complex problems with dependent variables, a novel physics-based pruning neural network (PbPNN) approach is proposed. The PbPNN innovatively performs network pruning based on the properties of unconditional and conditional variances. Through the mask matrix of specific settings, a pruning neural network with 3-dimensional outputs (an unconditional and two conditional responses) is constructed. The PbPNN method not only simultaneously calculates the unconditional and conditional variances but also effectively identifies the contributions from variable dependencies and interactions. Furthermore, the PbPNN method remains unaffected by the dimensionality of the problem, making it well-suited for high-dimensional complex problems. The effectiveness and accuracy of the proposed method are demonstrated through three numerical examples, where the PbPNN outperformed traditional methods in both sensitivity quantification and computational efficiency. Two engineering examples further validate the method's potential, proving the value of combining machine learning with the properties of unconditional and conditional variances in GSA.