Acknowledgement
The research has been funded by the "Progetto Rocca PostDoctoral Fellowship".
References
- M.I. Radaideh, T. Kozlowski, Surrogate modeling of advanced computer simulations using deep Gaussian processes, Reliab. Eng. Syst. Saf. 195 (October 2019) (2020), 106731, https://doi.org/10.1016/j.ress.2019.106731.
- F. D'Auria, C. Camargo, O. Mazzantini, The Best Estimate Plus Uncertainty (BEPU) approach in licensing of current nuclear reactors, Nucl. Eng. Des. 248 (2012) 317-328, https://doi.org/10.1016/j.nucengdes.2012.04.002.
- X. Wu, T. Kozlowski, Inverse uncertainty quantification of reactor simulations under the Bayesian framework using surrogate models constructed by polynomial chaos expansion, Nucl. Eng. Des. 313 (2017) 29-52, https://doi.org/10.1016/j.nucengdes.2016.11.032.
- R.K. Tripathy, I. Bilionis, Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification, J. Comput. Phys. 375 (2018) 565-588, https://doi.org/10.1016/j.jcp.2018.08.036.
- M.I. Radaideh, T. Kozlowski, Analyzing nuclear reactor simulation data and uncertainty with the group method of data handling, Nucl. Eng. Technol. 52 (2) (2020) 287-295, https://doi.org/10.1016/j.net.2019.07.023.
- P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems, SIAM Rev. 57 (4) (2015) 483-531, https://doi.org/10.1137/130932715.
- S. Chaturantabut, D.C. Sorensen, Nonlinear model reduction via discrete empirical interpolation, SIAM J. Sci. Comput. 32 (5) (2010) 2737-2764. https://doi.org/10.1137/090766498
- C. Worrell, L. Luangkesorn, J. Haight, T. Congedo, Machine learning of fire hazard model simulations for use in probabilistic safety assessments at nuclear power plants, Reliab. Eng. Syst. Saf. 183 (February 2018) (2019) 128-142, https://doi.org/10.1016/j.ress.2018.11.014.
- J.E. Hurtado, Filtered importance sampling with support vector margin: a powerful method for structural reliability analysis, Struct. Saf. 29 (1) (2007) 2-15, https://doi.org/10.1016/j.strusafe.2005.12.002.
- G. Roma, F. Antonello, F. Di Maio, N. Pedroni, E. Zio, A. Bersano, C. Bertani, F. Mascari, Passive safety systems analysis: a novel approach for inverse uncertainty quantification based on Stacked Sparse Autoencoders and Kriging metamodeling, Prog. Nucl. Energy 148 (September 2021) (2022), 104209, https://doi.org/10.1016/j.pnucene.2022.104209.
- S. Yoon, M.J. Kim, S. Park, G.Y. Kim, Thermal conductivity prediction model for compacted bentonites considering temperature variations, Nucl. Eng. Technol. 53 (10) (2021) 3359-3366, https://doi.org/10.1016/j.net.2021.05.001.
- J.P. Yurko, J. Buongiorno, R. Youngblood, Demonstration of emulator-based bayesian calibration of safety analysis codes: theory and formulation, Sci. Technol. Nucl. Instal. 2015 (2015), https://doi.org/10.1155/2015/839249. Mcmc).
- B. Ebiwonjumi, C. Kong, P. Zhang, A. Cherezov, D. Lee, Uncertainty quantification of PWR spent fuel due to nuclear data and modeling parameters, Nucl. Eng. Technol. 53 (3) (2021) 715-731, https://doi.org/10.1016/j.net.2020.07.012.
- B. Sudret, C.V. Mai, Computing derivative-based global sensitivity measures using polynomial chaos expansions, Reliab. Eng. Syst. Saf. 134 (2015) 241-250, https://doi.org/10.1016/j.ress.2014.07.009.
- L. Puppo, N. Pedroni, F. Di Maio, A. Bersano, C. Bertani, E. Zio, A framework based on finite mixture models and adaptive kriging for characterizing non-smooth and multimodal failure regions in a nuclear passive safety system, Reliab. Eng. Syst. Saf. 216 (August) (2021), 107963, https://doi.org/10.1016/j.ress.2021.107963.
- N. Pedroni, E. Zio, An Adaptive Metamodel-Based Subset Importance Sampling approach for the assessment of the functional failure probability of a thermal-hydraulic passive system, Appl. Math. Model. 48 (2017) 269-288, https://doi.org/10.1016/j.apm.2017.04.003.
- X. Song, L. Lv, W. Sun, J. Zhang, A radial basis function-based multi-fidelity surrogate model: exploring correlation between high-fidelity and low-fidelity models, Struct. Multidiscip. Optim. 60 (3) (2019) 965-981, https://doi.org/10.1007/s00158-019-02248-0.
- L. Conner, C.L. Worrell, J.P. Spring, J. Liao, Machine learned metamodeling of a computationally intensive accident simulation code, Int. Conf. Nucl. Eng. Proc., ICONE 1 (2021) 1-6, https://doi.org/10.1115/ICONE28-66619.
- R. Abu Saleem, M.I. Radaideh, T. Kozlowski, Application of deep neural networks for high-dimensional large BWR core neutronics, Nucl. Eng. Technol. 52 (12) (2020) 2709-2716, https://doi.org/10.1016/j.net.2020.05.010.
- L. Sun, H. Gao, S. Pan, J.X. Wang, Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data, Comput. Methods Appl. Mech. Eng. 361 (2020), 112732, https://doi.org/10.1016/j.cma.2019.112732.
- A. Ayodeji, M.A. Amidu, S.A. Olatubosun, Y. Addad, H. Ahmed, Deep learning for safety assessment of nuclear power reactors: reliability, explainability, and research opportunities, Prog. Nucl. Energy 151 (August) (2022), 104339, https://doi.org/10.1016/j.pnucene.2022.104339.
- V. Ciriello, V. Di Federico, M. Riva, F. Cadini, J. De Sanctis, E. Zio, A. Guadagnini, Polynomial chaos expansion for global sensitivity analysis applied to a model of radionuclide migration in a randomly heterogeneous aquifer, Stoch. Environ. Res. Risk Assess. 27 (4) (2013) 945-954, https://doi.org/10.1007/s00477-012-0616-7.
- F. Shriver, C. Gentry, J. Watson, Prediction of neutronics parameters within a two-dimensional reflective PWR assembly using deep learning, Nucl. Sci. Eng. 195 (6) (2021) 626-647, https://doi.org/10.1080/00295639.2020.1852021.
- M.I. Radaideh, D. Price, T. Kozlowski, Modeling nuclear data uncertainties using deep neural networks, in: International Conference on Physics of Reactors: Transition to a Scalable Nuclear Future, PHYSOR 2020, 2020-March, 2020, pp. 2583-2590, https://doi.org/10.1051/epjconf/202124715016.
- F. Cadini, A. Gioletta, E. Zio, Improved metamodel-based importance sampling for the performance assessment of radioactive waste repositories, Reliab. Eng. Syst. Saf. 134 (2015) 188e197, https://doi.org/10.1016/j.ress.2014.10.018.
- D. Price, M.I. Radaideh, B. Kochunas, Multiobjective optimization of nuclear microreactor reactivity control system operation with swarm and evolutionary algorithms, Nucl. Eng. Des. 393 (January) (2022), 111776, https://doi.org/10.1016/j.nucengdes.2022.111776.
- H. Kim, J. Cho, J. Park, Application of a deep learning technique to the development of a fast accident scenario identifier, IEEE Access 8 (2020) 177363-177373, https://doi.org/10.1109/ACCESS.2020.3026104.
- S. Ryu, H. Kim, S.G. Kim, K. Jin, J. Cho, J. Park, Probabilistic deep learning model as a tool for supporting the fast simulation of a thermal-hydraulic code, Expert Syst. Appl. 200 (March) (2022), 116966, https://doi.org/10.1016/j.eswa.2022.116966.
- M. Ebad Sichani, J.E. Padgett, V. Bisadi, Probabilistic seismic analysis of concrete dry cask structures, Struct. Saf. 73 (June 2017) (2018) 87-98, https://doi.org/10.1016/j.strusafe.2018.03.001.
- R. Shrestha, T. Kozlowski, Inverse uncertainty quantification of input model parameters for thermal-hydraulics simulations using expectation-maximization under Bayesian framework, J. Appl. Stat. 43 (6) (2016) 1011-1026, https://doi.org/10.1080/02664763.2015.1089220.
- A. Barredo Arrieta, N. Diaz-Rodriguez, J. Del Ser, A. Bennetot, S. Tabik, A. Barbado, S. Garcia, S. Gil-Lopez, D. Molina, R. Benjamins, R. Chatila, F. Herrera, Explainable Artificial Intelligence (XAI): concepts, taxonomies, opportunities and challenges toward responsible AI, Inf. Fusion 58 (October 2019) (2020) 82-115, https://doi.org/10.1016/j.inffus.2019.12.012.
- G.E. Karniadakis, I.G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, L. Yang, Physics-informed machine learning, Nat. Rev. Phys. 3 (6) (2021) 422-440, https://doi.org/10.1038/s42254-021-00314-5.
- M. Raissi, P. Perdikaris, G.E. Karniadakis, Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, J. Comput. Phys. 378 (2019) 686-707, https://doi.org/10.1016/j.jcp.2018.10.045.
- S. Cai, Z. Wang, S. Wang, P. Perdikaris, G.E. Karniadakis, Physics-informed neural networks for heat transfer problems, J. Heat Tran. 143 (6) (2021), https://doi.org/10.1115/1.4050542.
- E. Schiassi, M. De Florio, B.D. Ganapol, P. Picca, R. Furfaro, Physics-informed neural networks for the point kinetics equations for nuclear reactor dynamics, Ann. Nucl. Energy 167 (2022), 108833, https://doi.org/10.1016/j.anucene.2021.108833.
- E. Haghighat, M. Raissi, A. Moure, H. Gomez, R. Juanes, A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics, Comput. Methods Appl. Mech. Eng. 379 (2021), 113741, https://doi.org/10.1016/j.cma.2021.113741.
- Y. Lu, B. Wang, Y. Zhao, X. Yang, L. Li, M. Dong, Q. Lv, F. Zhou, N. Gu, L. Shang, Physics-informed surrogate modeling for hydro-fracture geometry prediction based on deep learning, Energy 253 (2022), 124139, https://doi.org/10.1016/j.energy.2022.124139.
- J. Buongiorno, B. Carmichael, B. Dunkin, J. Parsons, D. Smit, Can nuclear batteries Be economically competitive in large markets? Energies 14 (14) (2021) 4385, https://doi.org/10.3390/en14144385.
- F. Antonello, J. Buongiorno, E. Zio, A methodology to perform dynamic risk assessment using system theory and modeling and simulation: application to nuclear batteries, Reliab. Eng. Syst. Saf. 228 (August) (2022), 108769, https://doi.org/10.1016/j.ress.2022.108769.
- F. Antonello, J. Buongiorno, E. Zio, Insights in the safety analysis of an early microreactor design, Nucl. Eng. Des. 404 (September 2022) (2023), 112203, https://doi.org/10.1016/j.nucengdes.2023.112203.
- E. Zio, Prognostics and Health Management (PHM): where are we and where do we (need to) go in theory and practice, Reliab. Eng. Syst. Saf. 218 (October 2021) (2022), https://doi.org/10.1016/j.ress.2021.108119.
- A.F. Henry, The application of reactor kinetics to the analysis of experiments, Nucl. Sci. Eng. 3 (1) (1958) 52-70, https://doi.org/10.13182/nse58-1.
- D.P. Kingma, J.L. Ba, Adam: a method for stochastic optimization, 3rd Int. Conf. Learn. Represent. ICLR 2015 - Conf.Track Proc. (2015) 1-15.
- D. Pedamonti, Comparison of Non-linear Activation Functions for Deep Neural Networks on MNIST Classification Task, vol. 3, 2018. http://arxiv.org/abs/1804.02763.
- C. Cortes, G. Research, N. York, L 2 regularization for learning kernels, in: Twenty-Fifth Conference on Uncertainty in Artificial Intelligence, 2004, pp. 109-116.