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DOE OSTI · 2572736

The tensor-train stochastic finite volume method for uncertainty quantification

Walton, Steven [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000223434149)·Tokareva, Svetlana [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000256666173)·Manzini, Gianmarco [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000336263112)
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Abstract

The stochastic finite volume method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. Still, it struggles with the curse of dimensionality when dealing with multiple stochastic variables. Here, we introduce the stochastic finite volume method within the tensor-train framework to counteract this limitation. This integration, however, comes with its own set of difficulties, mainly due to the propensity for shock formation in hyperbolic systems. To overcome these issues, we have developed a tensor-train-adapted stochastic finite volume method that employs a global WENO reconstruction, making it suitable for such complex systems. This approach represents the first step in designing tensor-train techniques for hyperbolic systems and conservation laws involving shocks.

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97 MATHEMATICS AND COMPUTINGConservation lawsDiscontinuous solutionsHyperbolic systemsLow-rank approximationShocksStochastic finite volume methodTensor-train decompositionUncertainty quantification

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Walton, Steven [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000223434149), Tokareva, Svetlana [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000256666173), Manzini, Gianmarco [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000336263112). 2025-06-22. The tensor-train stochastic finite volume method for uncertainty quantification. https://doi.org/10.1016/j.jcp.2025.114192

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