About: Trend to Equilibrium for the Kinetic Fokker-Planck Equation via the Neural Network Approach

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Attributes	Values
type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
has title	Trend to Equilibrium for the Kinetic Fokker-Planck Equation via the Neural Network Approach
Creator	Lee, Jae Hwang, Hwang, Hyung Hyung, J Jang, Jin Jo, Hyeontae
Source	PMC
abstract	The issue of the relaxation to equilibrium has been at the core of the kinetic theory of rarefied gas dynamics. In the paper, we introduce the Deep Neural Network (DNN) approximated solutions to the kinetic Fokker-Planck equation in a bounded interval and study the large-time asymptotic behavior of the solutions and other physically relevant macroscopic quantities. We impose the varied types of boundary conditions including the inflow-type and the reflection-type boundaries as well as the varied diffusion and friction coefficients and study the boundary effects on the asymptotic behaviors. These include the predictions on the large-time behaviors of the pointwise values of the particle distribution and the macroscopic physical quantities including the total kinetic energy, the entropy, and the free energy. We also provide the theoretical supports for the pointwise convergence of the neural network solutions to the a priori analytic solutions. We use the library PyTorch, the activation function tanh between layers, and the Adam optimizer for the Deep Learning algorithm.
has issue date	2020-06-10(xsd:dateTime)
bibo:doi	10.1016/j.jcp.2020.109665
has license	no-cc
sha1sum (hex)	ce34a9e43f69be00e826b53b0bbf51076bfaf5d0
schema:url	https://doi.org/10.1016/j.jcp.2020.109665
resource representing a document's title	Trend to Equilibrium for the Kinetic Fokker-Planck Equation via the Neural Network Approach
has PubMed Central identifier	PMC7286285
schema:publication	J Comput Phys
resource representing a document's body	covid:ce34a9e43f69be00e826b53b0bbf51076bfaf5d0#body_text
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