Modeling neutronic transients with Galerkin projection onto a greedy-sampled, POD subspace

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

“…At every time step, the solution to Eq. ( 81) can be used in the expansion (74) to obtain the normalized intensities over the entire phase space of the problem.…”

“…Neural networks have been used to obtain closures for P N -type systems of moment equations of the BTE [62,63]. Data-driven ROMs have also been created for particle transport problems in nuclear reactor-physics applications [64,65,66,67], including (i) pin-by-pin reactor calculations [68], (ii) reactor kinetics [69,70], (iii) molten salt fast reactor problems [71,72,73], (iv) problems with feedback from delayed neutron precursors [74,75,76], (v) problems with domain decomposition [77], and (vi) for generation of neutron flux and cross sections for light water reactors [78].…”

“…A new approach based on data-driven reduced-order models (ROMs) has been gaining popularity in recent years which make use of data-based methodologies to dimensionality reduction. Data-driven models have been developed for (i) linear particle transport problems [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] (ii) nonlinear RT problems [49,50,51,52,53,54,55,56,57,58,59,60], and (iii) various problems in nuclear reactor-physics [61,62,63,64,65,66,67,68,69,70,71]. The fundamental idea behind these ROMs is to leverage databases of solutions to their problems of interest (known a-priori) to develop some reduction in the dimensionality for their involved equations.…”