5 papers
BEACONS: Bounded-Error, Algebraically-Composable Neural Solvers for Partial Differential Equations
Jonathan Gorard, Ammar Hakim, James Juno
The traditional limitations of neural networks in reliably generalizing beyond the convex hulls of their training data present a significant problem for computational physics, in w…
Beyond GRMHD: A Robust Numerical Scheme for Extended, Non-Ideal General Relativistic Multifluid Simulations
Jonathan Gorard, James Juno, Ammar Hakim
The equations of general relativistic magnetohydrodynamics (GRMHD) have become the standard mathematical framework for modeling high-energy plasmas in curved spacetimes. However, t…
Hydrodynamic and Electromagnetic Discrepancies between Neutron Star and Black Hole Spacetimes
Jonathan Gorard, James Juno, Ammar Hakim
The exterior spacetime geometry surrounding an uncharged, spinning black hole in general relativity depends only upon its mass and spin. However, the exterior geometry surrounding…
Improved Dimensionality Reduction for Inverse Problems in Nuclear Fusion and High-Energy Astrophysics
Jonathan Gorard, Ammar Hakim, Hong Qin +2
Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from…
Shock with Confidence: Formal Proofs of Correctness for Hyperbolic Partial Differential Equation Solvers
Jonathan Gorard, Ammar Hakim
First-order systems of hyperbolic partial differential equations (PDEs) occur ubiquitously throughout computational physics, commonly used in simulations of fluid turbulence, shock…