Causal artificial neural network and its applications in engineering design

Abstract

Abstract To reduce the computational cost in engineering design, expensive high-fidelity simulation models are approximated by mathematical models, named as metamodels. Typical metamodeling methods assume that expensive simulation models are black-box functions. In this paper, in order to improve the accuracy of metamodels and reduce the cost of building metamodels, knowledge about engineering design problems is employed to help develop a novel metamodel, named as causal artificial neural network (causal-ANN). Cause–effect relations intrinsic to the design problem are employed to decompose an ANN into sub-networks and values of intermediate variables are utilized to train these sub-networks. By involving knowledge of the design problem, the accuracy of causal-ANN is higher than the traditional metamodeling methods that assume black-box functions. Additionally, one can identify attractive subspaces from the causal-ANN by leveraging the structure of the causal-ANN and the theory of Bayesian Networks. The impacts of fidelity of causal graphs and design variable correlations are also discussed in the paper. The engineering case studies demonstrate that the causal-ANN can be accurately constructed with a small number of expensive simulations, and attractive design subspaces can be identified directly from the causal-ANN.