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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Symmetry Analysis Using Symbolic Computation

The symmetry group of a system of differential equations reveals basic invariant properties of the underlying model and its solutions. In many cases symmetry groups have simple geometric interpretations that can be applied to simplify the model and determine certain classes of solutions explicitly. The general procedure to compute the symmetry group of a given system of differential equations follows a well-known algorithm. However, this procedure involves a large number of laborious and usually error-prone calculations, especially in the case of higher-order systems. The purpose of this report is explain how to use an existing software program designed to automate the major steps of this algorithm in order to calculate the symmetry group of any system of differential equations more efficiently.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Symbolic diagnostics to interpret and analyze neural network models

Embedded machine-learned models (EMLMs) have the promise to improve the predictive accuracy of engineering simulators in environments of national interest. EMLMs often comprise complex input-output maps (e.g., neural networks), which make them unamenable to rigorous analysis and generally difficult to interpret. In the face of decades of theory, this lack of interpretability is a significant barrier to building confidence in these models. This work outlines an approach to interpret EMLMs using sparse polynomial regression for comparison with theoretical understanding. To do so, we build on the concept of Locally Interpretable Model-agnostic Explanations (LIME) using physics-informed clustering, prototype selection, and library construction. While general, we demonstrate our method on tensor-basis neural networks used in Reynolds-Averaged Navier-Stokes simulations of hypersonic fluid flows. Results are presented for a simulated toy model and for direct numerical simulations (DNS) of turbulent flows over a flat plate.

97 MATHEMATICS AND COMPUTING↗