From the 1 of 10 linked papers with an AI index.
10 papers
Shock solutions for the one-dimensional information geometric regularization of compressible flow
William Barham, Brian K. Tran, Ben S. Southworth +1
The paper proves existence, uniqueness, and regularity of one‑dimensional shock‑type traveling wave solutions for the information geometric regularization of the compressible Euler…
Hamiltonian Information Geometric Regularization of the Compressible Euler Equations
William Barham, Brian K. Tran, Ben S. Southworth +1
The recently proposed information geometric regularization (IGR) was the first inviscid regularization of the multi-dimensional compressible Euler equations, which enabled the simu…
Galerkin Formulation of Path Integrals in Lattice Field Theory
Brian K. Tran, Ben S. Southworth
We present a mathematical framework for Galerkin formulations of path integrals in lattice field theory. The framework is based on using the degrees of freedom associated to a Gale…
HalluField: Detecting LLM Hallucinations via Field-Theoretic Modeling
Minh Vu, Brian K. Tran, Syed A. Shah +3
Large Language Models (LLMs) exhibit impressive reasoning and question-answering capabilities. However, they often produce inaccurate or unreliable content known as hallucinations.…
Preconditioning transformations of adjoint systems for evolution equations
Brian K. Tran, Ben S. Southworth, Hannah F. Blumhoefer +1
Achieving robust control and optimization in high-fidelity physics simulations is extremely challenging, especially for evolutionary systems whose solutions span vast scales across…
A Geometric Perspective on Kinetic Matter-Radiation Interaction and Moment Systems
Brian K. Tran, Joshua W. Burby, Ben S. Southworth
We provide a geometric perspective on the kinetic interaction of matter and radiation, based on a pair bracket approach. We discuss the interaction of kinetic theories via dissipat…