TY - JOUR
T1 - Physics-informed neural networks for the point kinetics equations for nuclear reactor dynamics
AU - Schiassi, Enrico
AU - De Florio, Mario
AU - Ganapol, Barry D.
AU - Picca, Paolo
AU - Furfaro, Roberto
N1 - Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2022/3
Y1 - 2022/3
N2 - The paper presents a novel approach based on Physics-Informed Neural Networks (PINNs) for the solution of Point Kinetics Equations (PKEs) with temperature feedback. The approach is based on a new framework developed by the authors, which combines PINNs with Theory of Functional Connections and Extreme Learning Machines in the so called Extreme Theory of Functional Connections (X-TFC). The accuracy of X-TFC is tested against a number of published benchmarks (including for non-linear PKEs), showing its performance both in terms of accuracy and computational time. One of the main advantages of the proposed framework is in its flexibility to adapt to a variety of problems with minimal changes in coding and, after the training of the network, in its ability to offer an analytical representation (by Neural Networks) of the solution at any desired time instant outside the initial discretization.
AB - The paper presents a novel approach based on Physics-Informed Neural Networks (PINNs) for the solution of Point Kinetics Equations (PKEs) with temperature feedback. The approach is based on a new framework developed by the authors, which combines PINNs with Theory of Functional Connections and Extreme Learning Machines in the so called Extreme Theory of Functional Connections (X-TFC). The accuracy of X-TFC is tested against a number of published benchmarks (including for non-linear PKEs), showing its performance both in terms of accuracy and computational time. One of the main advantages of the proposed framework is in its flexibility to adapt to a variety of problems with minimal changes in coding and, after the training of the network, in its ability to offer an analytical representation (by Neural Networks) of the solution at any desired time instant outside the initial discretization.
KW - Extreme learning machine
KW - Extreme theory of functional connections
KW - Functional interpolation
KW - Nuclear reactor dynamics
KW - Physics-informed neural networks
KW - Points kinetic equations
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U2 - 10.1016/j.anucene.2021.108833
DO - 10.1016/j.anucene.2021.108833
M3 - Article
AN - SCOPUS:85120777040
SN - 0306-4549
VL - 167
JO - Annals of Nuclear Energy
JF - Annals of Nuclear Energy
M1 - 108833
ER -