Solving the Boltzmann Equation with a Neural Sparse Representation
DOI10.1137/23m1558227arXiv2302.09233MaRDI QIDQ6154197
No author found.
Publication date: 19 March 2024
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2302.09233
singular value decompositionBoltzmann equationBGK modelcanonical polyadic decompositionquadratic collision
Artificial neural networks and deep learning (68T07) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Eigenvalues, singular values, and eigenvectors (15A18) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Boltzmann equations (35Q20) PDEs on graphs and networks (ramified or polygonal spaces) (35R02) Numerical methods for low-rank matrix approximation; matrix compression (65F55)
Cites Work
- Deterministic numerical solutions of the Boltzmann equation using the fast spectral method
- High order asymptotic preserving DG-IMEX schemes for discrete-velocity kinetic equations in a diffusive scaling
- Macroscopic transport equations for rarefied gas flows. Approximation methods in kinetic theory.
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Fast evaluation of the Boltzmann collision operator using data driven reduced order models
- Neural-network based collision operators for the Boltzmann equation
- Tensor methods for the Boltzmann-BGK equation
- Using neural networks to accelerate the solution of the Boltzmann equation
- Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation
- An adaptive dynamical low rank method for the nonlinear Boltzmann equation
- Approximation of the Boltzmann collision operator based on Hermite spectral method
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
- Learning invariance preserving moment closure model for Boltzmann-BGK equation
- Randomized Alternating Least Squares for Canonical Tensor Decompositions: Application to A PDE With Random Data
- A Micro-Macro Decomposition-Based Asymptotic-Preserving Scheme for the Multispecies Boltzmann Equation
- Fast algorithms for computing the Boltzmann collision operator
- Numerical methods for kinetic equations
- Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
- Uniformly accurate machine learning-based hydrodynamic models for kinetic equations
- A Fast Spectral Method for the Boltzmann Collision Operator with General Collision Kernels
- Dynamical Low‐Rank Approximation
- On the kinetic theory of rarefied gases
- A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
- Numerical solution of the Boltzmann equation with S-model collision integral using tensor decompositions
- Machine Learning Moment Closure Models for the Radiative Transfer Equation II: Enforcing Global Hyperbolicity in Gradient-Based Closures
- Asymptotic-preserving neural networks for multiscale time-dependent linear transport equations
- Unnamed Item
This page was built for publication: Solving the Boltzmann Equation with a Neural Sparse Representation
