From the 1 of 4 linked papers with an AI index.
4 papers
Analysis of Moment Closures Using -Divergences for Rarefied Dynamics with Binary Collisions and Their Galerkin Discretizations
Michael R. A. Abdelmalik, Irene M. Gamba, Torsten Kessler +1
This work introduces a robust deterministic framework for approximating solutions of the Boltzmann equation with binary collisions by discretizing their dependence on time, positio…
When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning
Hugo Melchers, Victorita Dolean, Michael Abdelmalik
The paper investigates which neural operator architectures can replace the coarse solve in two‑level preconditioners for discretised linear PDEs, finding that the Neural Green's Op…
Neural Green's Operators for Parametric Partial Differential Equations
Hugo Melchers, Joost Prins, Michael Abdelmalik
This work introduces a paradigm for constructing parametric neural operators that are derived from finite-dimensional representations of Green's operators for linear partial differ…
An optimal Petrov-Galerkin framework for operator networks
Philip Charles, Deep Ray, Yue Yu +7
The optimal Petrov-Galerkin formulation to solve partial differential equations (PDEs) recovers the best approximation in a specified finite-dimensional (trial) space with respect…