PreprintArticleVersion 1This version is not peer-reviewed
Introducing the Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations. II: Illustrative Application to Heat and Energy Transfer in the Nordheim-Fuchs Phenomenological Model for Reactor Safety
Version 1
: Received: 14 October 2024 / Approved: 14 October 2024 / Online: 15 October 2024 (12:34:43 CEST)
How to cite:
Cacuci, D. G. Introducing the Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations. II: Illustrative Application to Heat and Energy Transfer in the Nordheim-Fuchs Phenomenological Model for Reactor Safety. Preprints2024, 2024101118. https://doi.org/10.20944/preprints202410.1118.v1
Cacuci, D. G. Introducing the Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations. II: Illustrative Application to Heat and Energy Transfer in the Nordheim-Fuchs Phenomenological Model for Reactor Safety. Preprints 2024, 2024101118. https://doi.org/10.20944/preprints202410.1118.v1
Cacuci, D. G. Introducing the Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations. II: Illustrative Application to Heat and Energy Transfer in the Nordheim-Fuchs Phenomenological Model for Reactor Safety. Preprints2024, 2024101118. https://doi.org/10.20944/preprints202410.1118.v1
APA Style
Cacuci, D. G. (2024). Introducing the Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations. II: Illustrative Application to Heat and Energy Transfer in the Nordheim-Fuchs Phenomenological Model for Reactor Safety. Preprints. https://doi.org/10.20944/preprints202410.1118.v1
Chicago/Turabian Style
Cacuci, D. G. 2024 "Introducing the Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations. II: Illustrative Application to Heat and Energy Transfer in the Nordheim-Fuchs Phenomenological Model for Reactor Safety" Preprints. https://doi.org/10.20944/preprints202410.1118.v1
Abstract
This work presents an illustrative application of the newly developed “Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (2nd-FASAM-NODE)” methodology to determine most efficiently the exact expressions of the first- and second-order sensitivities of NODE-decoder responses to the neural net’s underlying parameters (weights and initial conditions). The application of the 2nd-FASAM-NODE methodology will be illustrated using the Nordheim-Fuchs phenomenological model for reactor safety, which describes a short-time self-limiting power transient in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted. The representative model responses that will be analyzed in this work include the model’s the time-dependent total energy released, neutron flux, temperature and thermal conductivity. The 2nd-FASAM-NODE methodology yields the exact expressions of the first-order sensitivities of these decoder responses with respect to the underlying uncertain model parameters and initial conditions, requiring just a single large-scale computation per response. Furthermore, 2nd-FASAM-NODE methodology yields the exact expressions of the second-order sensitivities of a model response requiring as few large-scale computations as there are features/functions of model parameters, thereby demonstrating its unsurpassed efficiency for performing sensitivity analysis of NODE-nets.
Keywords
neural ordinary differential equations; second-order adjoint sensitivity analysis; first-order and second-order sensitivities of decoder responses with respect to features of model parameters; Nordheim-Fuchs phenomenological model for reactor safety; energy release decoder response; heat transfer decoder response
Subject
Engineering, Safety, Risk, Reliability and Quality
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
