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Methods such as non-intrusive polynomial chaos (NIPC), and stochasticcollocation are frequently used for uncertainty propagation problems.Particularly for low-dimensional problems, these methods often use atensor-product grid for sampling the space of uncertain inputs. A limitation ofthis approach is that it encounters a significant challenge: the number ofsample points grows exponentially with the increase of uncertain inputs.Current strategies to mitigate computational costs abandon the tensor structureof sampling points, with the aim of reducing their overall count.Contrastingly, our investigation reveals that preserving the tensor structureof sample points can offer distinct advantages in specific scenarios. Notably,by manipulating the computational graph of the targeted model, it is feasibleto avoid redundant evaluations at the operation level to significantly reducethe model evaluation cost on tensor-grid inputs. This paper presents apioneering method: Accelerated Model Evaluations on Tensor grids usingComputational graph transformations (AMTC). The core premise of AMTC lies inthe strategic modification of the computational graph of the target model toalgorithmically remove the repeated evaluations on the operation level. Weimplemented the AMTC method within the compiler of a new modeling languagecalled the Computational System Design Language (CSDL). We demonstrate theeffectiveness of AMTC by using it with the full-grid NIPC method to solve threelow-dimensional UQ problems involving an analytical piston model, amultidisciplinary unmanned aerial vehicle design model, and a multi-point airtaxi mission analysis model, respectively. For all of the test problems, AMTCreduces the model evaluation cost by between 50% and 90%, making the full-gridNIPC the most efficacious method to use among the UQ methods implemented.

Accelerating model evaluations in uncertainty propagation on tensor grids using computational graph transformations