Efficient Uncertainty Propagation Through Computational Graph Modification and Automatic Code Generation

View Video Presentation: https://doi.org/10.2514/6.2022-3997.vid Uncertainty quantification (UQ) methods such as integration-based non-intrusive polynomial chaos (NIPC) and stochastic collocation often use a tensor-product grid to sample the space of random inputs. In these situations, the number of quadrature points increases exponentially with the number of uncertain inputs. If we view the model as a computational graph with only elementary functions and operations, the current framework evaluates each operation node in the graph for all of the quadrature points. However, each node in the model only has distinct values on the quadrature points from the uncertain inputs on which the operation's output depends. This means that the current framework could create many unnecessary repeated evaluations on certain operation nodes. In this paper, we propose a new method that uses a computational graph representation of the model to algorithmically remove these unnecessary repeated evaluations so that the evaluation cost on full-grid quadrature points can be significantly reduced. This method is implemented in the Computational System Design Language, an algebraic modeling language, to achieve the cost reduction on UQ problems in a general way. The process of detecting and achieving savings from the model structure is abstracted by the modeling language and its back-end. This method is applied to a multi-point aircraft mission analysis problem with two uncertain inputs. Our method reduces the computing time of the integration-based NIPC method by an order of magnitude. For a wide range of forward UQ problems, we expect this method to significantly improve time scaling with the number of the uncertain inputs.