59 citations · 115 across the 7 of their papers we have counts for
7 papers
Parameter Estimation with Maximal Updated Densities
Michael Pilosov, Carlos del-Castillo-Negrete, Tian Yu Yen +2
A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i…
Learning Quantities of Interest from Dynamical Systems for Observation-Consistent Inversion
Steven Mattis, Kyle Robert Steffen, Troy Butler +2
Dynamical systems arise in a wide variety of mathematical models from science and engineering. A common challenge is to quantify uncertainties on model inputs (parameters) that cor…
Convergence of Probability Densities using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification: Extensions to
Troy Butler, Tim Wildey, Wenjuan Zhang
A previous study analyzed the convergence of probability densities for forward and inverse problems when a sequence of approximate maps between model inputs and outputs converges i…
Convergence of Probability Densities using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification
T. Butler, J. D. Jakeman, T. Wildey
We analyze the convergence of probability density functions utilizing approximate models for both forward and inverse problems. We consider the standard forward uncertainty quantif…
A Consistent Bayesian Formulation for Stochastic Inverse Problems Based on Push-forward Measures
T. Butler, J. D. Jakeman, T. Wildey
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of int…
Quantifying Uncertainty in Material Damage from Vibrational Data
Troy Butler, Antti Huhtala, Mika Juntunen
The response of a vibrating beam to a force depends on many physical parameters including those determined by material properties. Damage caused by fatigue or cracks result in loca…
Solving Stochastic Inverse Problems using Sigma-Algebras on Contour Maps
Troy Butler, Don Estep, Simon Tavener +3
We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the pr…