Physics-based loss and machine learning approach in application to non-Newtonian fluids flow modeling
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Physics-based loss and machine learning approach in application to non-Newtonian fluids flow modeling. / Kornaeva, Elena; Kornaev, Alexey; Fetisov, Alexander; Stebakov, Ivan; Ibragimov, Bulat.
2022 IEEE Congress on Evolutionary Computation, CEC 2022 - Conference Proceedings. IEEE, 2022.Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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TY - GEN
T1 - Physics-based loss and machine learning approach in application to non-Newtonian fluids flow modeling
AU - Kornaeva, Elena
AU - Kornaev, Alexey
AU - Fetisov, Alexander
AU - Stebakov, Ivan
AU - Ibragimov, Bulat
N1 - Publisher Copyright: © 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - The variational approach of finding the extremum of an objective functional is an alternative approach to the solution of partial differential equations in mechanics of continua. The great challenge in the calculus of variations direct methods is to find a set of functions that will be able to approximate the solution accurately enough. Artificial neural networks are a powerful tool for approximation, and the physics-based functional can be the natural loss for a machine learning method. In this paper, we focus on the loss that may take non-linear fluid properties and mass forces into account. We modified the energy-based variational principle and determined the constraints on its unknown functions that implement boundary conditions. We explored artificial neural networks as an option for loss minimization and the approximation of the unknown functions. We compared the obtained results with the known solutions. The proposed method allows modeling non-Newtonian fluids flow including blood, synthetic oils, paints, plastic, bulk materials, and even rheomagnetic fluids. The fluids flow velocity approximation error was up to 4% in comparison with the analytical and numerical solutions.
AB - The variational approach of finding the extremum of an objective functional is an alternative approach to the solution of partial differential equations in mechanics of continua. The great challenge in the calculus of variations direct methods is to find a set of functions that will be able to approximate the solution accurately enough. Artificial neural networks are a powerful tool for approximation, and the physics-based functional can be the natural loss for a machine learning method. In this paper, we focus on the loss that may take non-linear fluid properties and mass forces into account. We modified the energy-based variational principle and determined the constraints on its unknown functions that implement boundary conditions. We explored artificial neural networks as an option for loss minimization and the approximation of the unknown functions. We compared the obtained results with the known solutions. The proposed method allows modeling non-Newtonian fluids flow including blood, synthetic oils, paints, plastic, bulk materials, and even rheomagnetic fluids. The fluids flow velocity approximation error was up to 4% in comparison with the analytical and numerical solutions.
KW - calculus of variations
KW - continuum mechanics
KW - convolutional neural network
KW - differentiable physics
KW - loss
KW - multilayer perceptron
KW - physics-based machine learning
KW - variational principle
UR - http://www.scopus.com/inward/record.url?scp=85138703496&partnerID=8YFLogxK
U2 - 10.1109/CEC55065.2022.9870411
DO - 10.1109/CEC55065.2022.9870411
M3 - Article in proceedings
AN - SCOPUS:85138703496
BT - 2022 IEEE Congress on Evolutionary Computation, CEC 2022 - Conference Proceedings
PB - IEEE
T2 - 2022 IEEE Congress on Evolutionary Computation, CEC 2022
Y2 - 18 July 2022 through 23 July 2022
ER -
ID: 322573808