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Machine Learning Moment Closure Models for the Radiative Transfer Equation II: Enforcing Global Hyperbolicity in Gradient-Based Closures

Journal Article · · Multiscale Modeling & Simulation
DOI:https://doi.org/10.1137/21m1423956· OSTI ID:2420674
 [1];  [2];  [3];  [4];  [5]
  1. Department of Mathematics, Michigan State University, East Lansing, MI 48824 USA.; OSTI
  2. Department of Mathematics, Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI 48824 USA.
  3. Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI 48824 USA.
  4. National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 USA.
  5. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China, and Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, China.

Not provided.

Research Organization:
Michigan State Univ., East Lansing, MI (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0017955
OSTI ID:
2420674
Journal Information:
Multiscale Modeling & Simulation, Journal Name: Multiscale Modeling & Simulation Journal Issue: 2 Vol. 21; ISSN 1540-3459
Publisher:
SIAM
Country of Publication:
United States
Language:
English

References (42)

High-Order Entropy-Based Closures for Linear Transport in Slab Geometry II: A Computational Study of the Optimization Problem journal January 2012
Approximating the $M_2$ method by the extended quadrature method of moments for radiative transfer in slab geometry journal March 2016
Relating Eddington factors to flux limiters journal February 1984
Hybrid methods for radiation transport using diagonally implicit Runge–Kutta and space–time discontinuous Galerkin time integration journal January 2019
Neural network representability of fully ionized plasma fluid model closures journal July 2020
Deep learning surrogate model for kinetic Landau-fluid closure with collision journal July 2020
Evaluation of quadrature schemes for the discrete ordinates method journal April 2004
Uniformly accurate machine learning-based hydrodynamic models for kinetic equations journal October 2019
Linear Stability of Hyperbolic Moment Models for Boltzmann Equation journal May 2017
Perturbed, entropy-based closure for radiative transfer journal January 2013
Robust and accurate filtered spherical harmonics expansions for radiative transfer journal August 2010
Optical tomography using the time-independent equation of radiative transfer — Part 1: forward model journal March 2002
Machine learning moment closure models for the radiative transfer equation I: Directly learning a gradient based closure journal March 2022
Conservation-dissipation formalism of irreversible thermodynamics journal January 2015
On the kinetic theory of rarefied gases journal December 1949
Hyperbolic-Parabolic Singular Limits for First-Order Nonlinear Systems journal April 2001
Direct Flux Gradient Approximation to Moment Closure of Kinetic Equations journal January 2021
Efficient Implementation of Weighted ENO Schemes journal June 1996
Implicit filtered P for high-energy density thermal radiation transport using discontinuous Galerkin finite elements journal September 2016
Machine learning surrogate models for Landau fluid closure journal April 2020
Uniform global existence and parabolic limit for partially dissipative hyperbolic systems journal May 2016
Machine Learning Moment Closure Models for the Radiative Transfer Equation III: Enforcing Hyperbolicity and Physical Characteristic Speeds journal November 2022
A neural network closure for the Euler-Poisson system based on kinetic simulations journal January 2022
Adaptive change of basis in entropy-based moment closures for linear kinetic equations journal February 2014
A nonlinear moment model for radiative transfer equation in slab geometry journal March 2020
Learning Thermodynamically Stable and Galilean Invariant Partial Differential Equations for Non-Equilibrium Flows journal May 2021
An arbitrary-order, fully implicit, hybrid kinetic solver for linear radiative transport using integral deferred correction journal October 2017
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II journal July 1989
Positive $P_N$ Closures journal January 2010
An interesting class of partial differential equations journal March 2008
Discovering governing equations from data by sparse identification of nonlinear dynamical systems journal March 2016
Singular Perturbations of First-Order Hyperbolic Systems with Stiff Source Terms journal June 1999
Globally hyperbolic regularization of Grad’s moment system in one-dimensional space journal January 2013
On hyperbolicity of 13-moment system journal January 2014
Globally Hyperbolic Regularization of Grad's Moment System journal July 2013
Analytic closures for M1 neutrino transport journal April 2017
Solving high-dimensional partial differential equations using deep learning journal August 2018
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations journal February 2019
A Nonlinear Hyperbolic Model for Radiative Transfer Equation in Slab Geometry journal January 2020
On the Radiative Equilibrium of a Stellar Atmosphere. journal March 1944
High-order entropy-based closures for linear transport in slab geometry journal January 2011
Efficient implementation of essentially non-oscillatory shock-capturing schemes journal August 1988

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