A Machine Learning Approach To Calculating the Non-Equilibrium Diffusion Coefficients in the State-To-State Solution of the Navier–Stokes Equations

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A Machine Learning Approach To Calculating the Non-Equilibrium Diffusion Coefficients in the State-To-State Solution of the Navier–Stokes Equations. / Kiva, Pavel ; Grafeeva, Natalia ; Mikhailova, Elena .

In: Lobachevskii Journal of Mathematics, Vol. 44, No. 1, 17.05.2023, p. 170-177.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{fe371cde04de4b4b9b737395d77adcf2,

title = "A Machine Learning Approach To Calculating the Non-Equilibrium Diffusion Coefficients in the State-To-State Solution of the Navier–Stokes Equations",

abstract = "This work considers the application of machine learning methods for approximate determination of diffusion coefficients that are part of extended Navier–Stokes equations solved in a state-by-state approximation. Three methods are suggested: the k-Nearest Neighbors (k-NN) algorithm, a classical neural network (NN) and Physics-Informed Neural Network (PINN). The resulting solution, fully based on data and well-known physics relations, can be used to direct research in more complex cases.",

keywords = "Neural Networks, PINNs, k-NN, Navier–Stokes equations",

author = "Pavel Kiva and Natalia Grafeeva and Elena Mikhailova",

note = "Kiva, P., Grafeeva, N. & Mikhailova, E. A Machine Learning Approach To Calculating the Non-Equilibrium Diffusion Coefficients in the State-To-State Solution of the Navier–Stokes Equations. Lobachevskii J Math 44, 170–177 (2023). https://doi.org/10.1134/S1995080223010213",

year = "2023",

month = may,

day = "17",

doi = "10.1134/s1995080223010213",

language = "English",

volume = "44",

pages = "170--177",

journal = "Lobachevskii Journal of Mathematics",

issn = "1995-0802",

publisher = "Pleiades Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - A Machine Learning Approach To Calculating the Non-Equilibrium Diffusion Coefficients in the State-To-State Solution of the Navier–Stokes Equations

AU - Kiva, Pavel

AU - Grafeeva, Natalia

AU - Mikhailova, Elena

N1 - Kiva, P., Grafeeva, N. & Mikhailova, E. A Machine Learning Approach To Calculating the Non-Equilibrium Diffusion Coefficients in the State-To-State Solution of the Navier–Stokes Equations. Lobachevskii J Math 44, 170–177 (2023). https://doi.org/10.1134/S1995080223010213

PY - 2023/5/17

Y1 - 2023/5/17

N2 - This work considers the application of machine learning methods for approximate determination of diffusion coefficients that are part of extended Navier–Stokes equations solved in a state-by-state approximation. Three methods are suggested: the k-Nearest Neighbors (k-NN) algorithm, a classical neural network (NN) and Physics-Informed Neural Network (PINN). The resulting solution, fully based on data and well-known physics relations, can be used to direct research in more complex cases.

AB - This work considers the application of machine learning methods for approximate determination of diffusion coefficients that are part of extended Navier–Stokes equations solved in a state-by-state approximation. Three methods are suggested: the k-Nearest Neighbors (k-NN) algorithm, a classical neural network (NN) and Physics-Informed Neural Network (PINN). The resulting solution, fully based on data and well-known physics relations, can be used to direct research in more complex cases.

KW - Neural Networks

KW - PINNs

KW - k-NN

KW - Navier–Stokes equations

UR - https://www.mendeley.com/catalogue/c3e4e19a-cb0f-33f9-8c3e-2f55b3d0fdee/

U2 - 10.1134/s1995080223010213

DO - 10.1134/s1995080223010213

M3 - Article

VL - 44

SP - 170

EP - 177

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 1

ER -

ID: 106487604