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We propose semi-intrusive low-rank model reduction strategies for time-dependent neutron transport problems. Starting from a full-order discretization of the transport equation in space and angle, we construct reduced models based on both linear subspaces and nonlinear manifold approaches. The nonlinear framework employs quadratic lifting maps (element-wise and tensorial) that embed low-dimensional latent variables into higher-dimensional lifted coordinates, thereby enhancing the expressive power of the reduced model. To avoid the prohibitive cost of forming and projecting advection operators, we introduce a data-driven operator inference strategy that directly estimates reduced advection operators from high-fidelity simulation data, while reaction operators are obtained cheaply by projection. Numerical experiments on a one-dimensional slab benchmark and on a two-dimensional clustered-inclusions benchmark generated with the OpenSn solver assess the proposed framework. In the one-dimensional case, where projected and inferred streaming operators can be compared directly, tensorial lifting delivers markedly improved accuracy compared to linear and element-wise quadratic reductions at comparable latent dimensions, while maintaining significant computational speed-ups. In the two-dimensional case, where the full streaming operator is not explicitly accessible, the semi-intrusive formulation remains applicable and tensorial manifold reduction provides the most accurate reduced solutions at small-to-moderate latent dimensions. These results highlight the potential of combining nonlinear manifold reduction with operator inference to obtain efficient and accurate surrogate models for neutron transport dynamics in large-scale, multi-dimensional settings.
Silva et al. (Thu,) studied this question.