A nonintrusive adaptive reduced order modeling approach for a molten salt reactor system

Abstract We use a novel nonintrusive adaptive Reduced Order Modeling method to build a reduced model for a molten salt reactor system. Our approach is based on Proper Orthogonal Decomposition combined with locally adaptive sparse grids. Our reduced model captures the effect of 27 model parameters on k eff of the system and the spatial distribution of the neutron flux and salt temperature. The reduced model was tested on 1000 random points. The maximum error in multiplication factor was found to be less than 50 pcm and the maximum L 2 error in the flux and temperature were less than 1%. Using 472 snapshots, the reduced model was able to simulate any point within the defined range faster than the high-fidelity model by a factor of 5 × 10 6 . We then employ the reduced model for uncertainty and sensitivity analysis of the selected parameters on k eff and the maximum temperature of the system.

[1]  Ngoc Cuong Nguyen,et al.  Gaussian functional regression for output prediction: Model assimilation and experimental design , 2016, J. Comput. Phys..

[2]  P. Nair,et al.  Reduced‐order modeling of parameterized PDEs using time–space‐parameter principal component analysis , 2009 .

[3]  H. Bungartz,et al.  Sparse grids , 2004, Acta Numerica.

[4]  Michael Griebel,et al.  Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences , 1998, Computing.

[5]  Gianluigi Rozza,et al.  Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics , 2014 .

[6]  Yoshua Bengio,et al.  Pattern Recognition and Neural Networks , 1995 .

[7]  Christopher C. Pain,et al.  A POD reduced‐order model for eigenvalue problems with application to reactor physics , 2013 .

[8]  H. Tran,et al.  Modeling and control of physical processes using proper orthogonal decomposition , 2001 .

[9]  Karen Willcox,et al.  A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems , 2015, SIAM Rev..

[10]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[11]  Paola Annoni,et al.  Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index , 2010, Comput. Phys. Commun..

[12]  D. Sorensen,et al.  A Survey of Model Reduction Methods for Large-Scale Systems , 2000 .

[13]  Gianluigi Rozza,et al.  A reduced order model for investigating the dynamics of the Gen-IV LFR coolant pool , 2017 .

[14]  Jan S. Hesthaven,et al.  Non-intrusive reduced order modeling of nonlinear problems using neural networks , 2018, J. Comput. Phys..

[15]  Jean C. Ragusa,et al.  Reduced-order modeling of parameterized multi-group diffusion k-eigenvalue problems , 2019 .

[16]  Erich Novak,et al.  High dimensional polynomial interpolation on sparse grids , 2000, Adv. Comput. Math..

[17]  Vladimir Buljak.  Inverse Analyses with Model Reduction: Proper Orthogonal Decomposition in Structural Mechanics , 2011 .

[18]  Danny Lathouwers,et al.  A nonintrusive reduced order modelling approach using Proper Orthogonal Decomposition and locally adaptive sparse grids , 2019, J. Comput. Phys..

[19]  Antonio Hurtado,et al.  Reduced order modeling of a natural circulation system by proper orthogonal decomposition , 2019 .

[20]  Axel Laureau.  Développement de modèles neutroniques pour le couplage thermohydraulique du MSFR et le calcul de paramètres cinétiques effectifs , 2015 .

[21]  M. Aufiero,et al.  Molten salt fast reactors , 2016 .