57 citations · 131 across the 64 of their papers we have counts for
70 papers
Inner Momentum for Differentially Private Muon
Bishnu Bhusal, Minh Vu, Ben Southworth +3
Differentially private training clips each per-example gradient before adding noise. This clipping is radial for each example, yet unequal clipping factors can distort the relative…
An Efficient Solver for Finite Element-based Constrained Transport in 3D Magnetohydrodynamics Applied to Magnetic Confinement Fusion
Golo A. Wimmer, Konstantin Lipnikov, Ben S. Southworth +1
We present an efficient solver framework for the stiff magnetic wave coupling arising in resistive magnetohydrodynamics (MHD) on realistic tokamak geometries. The approach builds o…
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…
Broken-space Additive Schwarz Mass Inverse Approximations and (Block) Preconditioning
Oliver A. Krzysik, Ben S. Southworth, Golo A. Wimmer
Finite-element mass matrix solves and approximate inverses arise often in explicit time integration as well as Schur-complement-based block preconditioning. A diagonal approximatio…
A black-box, multilevel algebraic preconditioning framework for conforming finite elements
O. A. Krzysik, B. S. Southworth, G. A. Wimmer
Recently we introduced the least-squares algebraic-multigrid domain-decomposition (LS-AMG-DD) method as a multilevel, algebraic preconditioner for sparse symmetric positive definit…
Two-level convergence of Algebraic Multigrid with Overlapping Smoothers and Spectral Coarse Grids
O. A. Krzysik, B. S. Southworth, H. Al Daas
We recently developed the least-squares algebraic-multigrid domain-decomposition (LS-AMG-DD) solver as an algebraic multilevel method for sparse symmetric positive definite matrice…
Muon in Vision Transformers: Optimizer-Recipe Interactions and Gradient Spectra
Ben S. Southworth, Shuai Jiang, Daniel McBride +2
Muon is a recently developed matrix-aware optimizer that has shown strong results in transformer training, but its behavior in vision transformers (ViTs) is not yet well understood…
Beyond Muon: MUD (MomentUm Decorrelation) for Faster Transformer Training
Ben S. Southworth, Stephen Thomas
Orthogonalized-momentum optimizers such as Muon improve transformer training by approximately whitening/orthogonalizing matrix-valued momentum updates via a short polar-decompositi…
Multilevel Training for Kolmogorov Arnold Networks
Ben S. Southworth, Jonas A. Actor, Graham Harper +1
Algorithmic speedup of training common neural architectures is made difficult by the lack of structure guaranteed by the function compositions inherent to such networks. In contras…
Algebraic Multigrid with Overlapping Schwarz Smoothers and Local Spectral Coarse Grids for Least Squares Problems
Ben S. Southworth, Hussam Al Daas, Golo A. Wimmer +1
This paper develops a new algebraic multigrid (AMG) method for sparse least-squares systems of the form motivated by challenging applications in scientific computing where…
On the Convergence Behavior of Preconditioned Gradient Descent Toward the Rich Learning Regime
Shuai Jiang, Alexey Voronin, Eric Cyr +1
Spectral bias, the tendency of neural networks to learn low frequencies first, can be both a blessing and a curse. While it enhances the generalization capabilities by suppressing…
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…
Preconditioning a hybridizable discontinuous Galerkin method for Navier-Stokes at high Reynolds number
Alexander D. Lindsay, Sander Rhebergen, Ben S. Southworth
We introduce a preconditioner for a hybridizable discontinuous Galerkin discretization of the linearized Navier-Stokes equations at high Reynolds number. The preconditioner is base…
Learning interpretable closures for thermal radiation transport in optically-thin media using WSINDy
Daniel Messenger, Ben Southworth, Hans Hammer +1
We introduce an equation learning framework to identify a closed set of equations for moment quantities in 1D thermal radiation transport (TRT) in optically thin media. While optic…
Multiscale Graph Reduction for Heterogeneous and Anisotropic Discrete Diffusion Processes
Maria Vasilyeva, James Brannick, Ben S. Southworth
We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a pa…
Causal Multi-fidelity Surrogate Forward and Inverse Models for ICF Implosions
Tyler E. Maltba, Ben S. Southworth, Jeffrey R. Haack +1
Continued progress in inertial confinement fusion (ICF) requires solving inverse problems relating experimental observations to simulation input parameters, followed by design opti…
Implicit-Explicit Scheme with Multiscale Vanka Two-Grid Solver for Heterogeneous Unsaturated Poroelasticity
Maria Vasilyeva, Ben S. Southworth, Yunhui He +1
We consider a coupled nonlinear system of equations that describe unsaturated flow in heterogeneous poroelastic media. For the numerical solution, we use a finite element approxima…
Learning robust parameter inference and density reconstruction in flyer plate impact experiments
Evan Bell, Daniel A. Serino, Ben S. Southworth +2
Estimating physical parameters or material properties from experimental observations is a common objective in many areas of physics and material science. In many experiments, espec…
ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized partial differential equations from sparse and noisy data
Aviral Prakash, Ben S. Southworth, Marc L. Klasky
Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized PDE systems are expensive due to the high computational…
Leveraging KANs for Expedient Training of Multichannel MLPs via Preconditioning and Geometric Refinement
Jonas A. Actor, Graham Harper, Ben Southworth +1
Multilayer perceptrons (MLPs) are a workhorse machine learning architecture, used in a variety of modern deep learning frameworks. However, recently Kolmogorov-Arnold Networks (KAN…
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…
Optimal transfer operators in algebraic two-level methods for nonsymmetric and indefinite problems
Oliver A. Krzysik, Ben S. Southworth, Golo A. Wimmer +3
Consider an algebraic two-level method applied to the -dimensional linear system using fine-space preconditioner (i.e., ``relaxation'' or ``smoother'…
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…
Generalized Optimal AMG Convergence Theory for Stokes Equations Using Smooth Aggregation and Vanka Relaxation Strategies
Ahsan Ali, James J. Brannick, Karsten Kahl +4
This paper discusses our recent generalized optimal algebraic multigrid (AMG) convergence theory applied to the steady-state Stokes equations discretized using Taylor-Hood elements…