4 citations · 7 across the 11 of their papers we have counts for
11 papers
Shock solutions for the one-dimensional information geometric regularization of compressible flow
William Barham, Brian K. Tran, Ben S. Southworth +1
The information geometric regularization (IGR) is an inviscid regularization of the compressible Euler equations that alters the geometry of Lagrangian characteristics to prevent t…
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…
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…
Multirate Runge-Kutta for Nonlinearly Partitioned Systems
Tommaso Buvoli, Brian K. Tran, Ben S. Southworth
Multirate integration is an increasingly relevant tool that enables scientists to simulate multiphysics systems. Existing multirate methods are designed for equations whose fast an…
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…
Variational Principles for Hamiltonian Systems
Brian K. Tran, Melvin Leok
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present…
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…
On Properties of Adjoint Systems for Evolutionary PDEs
Brian K. Tran, Ben S. Southworth, Melvin Leok
We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete lev…
Order Conditions for Nonlinearly Partitioned Runge-Kutta Methods
Brian K. Tran, Ben S. Southworth, Tommaso Buvoli
Recently a new class of nonlinearly partitioned Runge--Kutta (NPRK) methods was proposed for nonlinearly partitioned systems of autonomous ordinary differential equations, $y' = F(…
A Type II Hamiltonian Variational Principle and Adjoint Systems for Lie Groups
Brian K. Tran, Melvin Leok
We present a novel Type II variational principle on the cotangent bundle of a Lie group which enforces Type II boundary conditions, i.e., fixed initial position and final momentum.…