47 citations · 102 across the 10 of their papers we have counts for
13 papers
Source identification via pathwise gradient estimation
Richard B. Lehoucq, Scott A. McKinley, Petr Plecháč
In the context of PDE-constrained optimization theory, source identification problems traditionally entail particles emerging from an unknown source distribution inside a domain, m…
A Stochastic Calculus Approach to Boltzmann Transport
J. Darby Smith, Rich Lehoucq, Brian Franke
Traditional Monte Carlo methods for particle transport utilize source iteration to express the solution, the flux density, of the transport equation as a Neumann series. Our contri…
Optimal accuracy for linear sets of equations with the graph Laplacian
Richard B. Lehoucq, Michael Weylandt, Jonathan W. Berry
We show that certain Graph Laplacian linear sets of equations exhibit optimal accuracy, guaranteeing that the relative error is no larger than the norm of the relative residual and…
Inferring stochastic rates from heterogeneous snapshots of particle positions
Christopher E. Miles, Scott A. McKinley, Fangyuan Ding +1
Many imaging techniques for biological systems -- like fixation of cells coupled with fluorescence microscopy -- provide sharp spatial resolution in reporting locations of individu…
Zero-Truncated Poisson Regression for Sparse Multiway Count Data Corrupted by False Zeros
Oscar López, Daniel M. Dunlavy, Richard B. Lehoucq
We propose a novel statistical inference methodology for multiway count data that is corrupted by false zeros that are indistinguishable from true zero counts. Our approach consist…
Neuromorphic scaling advantages for energy-efficient random walk computation
J. Darby Smith, Aaron J. Hill, Leah E. Reeder +5
Computing stands to be radically improved by neuromorphic computing (NMC) approaches inspired by the brain's incredible efficiency and capabilities. Most NMC research, which aims t…
A Deterministic Hitting-Time Moment Approach to Seed-set Expansion over a Graph
Alexander H. Foss, Richard B. Lehoucq, W. Zachary Stuart +2
We introduce HITMIX, a new technique for network seed-set expansion, i.e., the problem of identifying a set of graph vertices related to a given seed-set of vertices. We use the mo…
Solving a steady-state PDE using spiking networks and neuromorphic hardware
J. Darby Smith, William Severa, Aaron J. Hill +5
The widely parallel, spiking neural networks of neuromorphic processors can enable computationally powerful formulations. While recent interest has focused on primarily machine lea…
Spiking Neural Algorithms for Markov Process Random Walk
William Severa, Rich Lehoucq, Ojas Parekh +1
The random walk is a fundamental stochastic process that underlies many numerical tasks in scientific computing applications. We consider here two neural algorithms that can be use…
Complex fracture nucleation and evolution with nonlocal elastodynamics
Robert Lipton, Stewart Silling, Richard Lehoucq
A mechanical model is introduced for predicting the initiation and evolution of complex fracture patterns without the need for a damage variable or law. The model, a continuum vari…
A Meshless Galerkin Method For Non-Local Diffusion Using Localized Kernel Bases
Richard B. Lehoucq, Francis J. Narcowich, Stephen T. Rowe +1
We introduce a meshless method for solving both continuous and discrete variational formulations of a volume constrained, nonlocal diffusion problem. We use the discrete solution t…
The exit-time problem for a Markov jump process
Nathanial Burch, Marta D'Elia, R. B. Lehoucq
The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its locatio…
A Nonlocal Strain Measure for Digital Image Correlation
R. B. Lehoucq, P. L. Reu, D. Z. Turner
We propose a nonlocal strain measure for use with digital image correlation (DIC). Whereas the traditional notion of compatibility (strain as the derivative of the displacement fie…