Separable Physics-informed Neural Networks for Solving the BGK Model of the Boltzmann Equation

arXiv:2403.06342v1 Announce Type: cross
Abstract: In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation. While the mesh-free nature of PINNs offers significant advantages in handling high-dimensional partial differential equations (PDEs), challenges arise when applying quadrature rules for accurate integral evaluation in the BGK operator, which can compromise the mesh-free benefit and increase computational costs. To address this, we leverage the canonical polyadic decomposition structure of …

abstract advantages arxiv boltzmann challenges cs.lg cs.na differential equation free math.na mesh nature networks neural networks physics physics-informed study type