19 citations · 19 across the 9 of their papers we have counts for
14 papers
Solving High-Dimensional Inverse Problems with Auxiliary Uncertainty via Operator Learning with Limited Data
Joseph Hart, Mamikon Gulian, Indu Manickam +1
In complex large-scale systems such as climate, important effects are caused by a combination of confounding processes that are not fully observable. The identification of sources…
A new perspective on parameter study of optimization problems
Alen Alexanderian, Joseph Hart, Mason Stevens
We provide a new perspective on the study of parameterized optimization problems. Our approach combines methods for post-optimal sensitivity analysis and ordinary differential equa…
Hyper-differential sensitivity analysis for nonlinear Bayesian inverse problems
Isaac Sunseri, Alen Alexanderian, Joseph Hart +1
We consider hyper-differential sensitivity analysis (HDSA) of nonlinear Bayesian inverse problems governed by PDEs with infinite-dimensional parameters. In previous works, HDSA has…
Enabling hyper-differential sensitivity analysis for ill-posed inverse problems
Joseph Hart, Bart van Bloemen Waanders
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain…
Train Like a (Var)Pro: Efficient Training of Neural Networks with Variable Projection
Elizabeth Newman, Lars Ruthotto, Joseph Hart +1
Deep neural networks (DNNs) have achieved state-of-the-art performance across a variety of traditional machine learning tasks, e.g., speech recognition, image classification, and s…
Hyper-Differential Sensitivity Analysis for Inverse Problems Constrained by Partial Differential Equations
Isaac Sunseri, Joseph Hart, Bart van Bloemen Waanders +1
High fidelity models used in many science and engineering applications couple multiple physical states and parameters. Inverse problems arise when a model parameter cannot be deter…
Randomized Algorithms for Generalized Singular Value Decomposition with Application to Sensitivity Analysis
Arvind K. Saibaba, Joseph Hart, Bart van Bloemen Waanders
The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is…
Hyper-Differential Sensitivity Analysis of Uncertain Parameters in PDE-Constrained Optimization
Joseph Hart, Bart van Bloemen Waanders, Roland Herzog
Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization…
Robustness of the Sobol' indices to marginal distribution uncertainty
Joseph Hart, Pierre Gremaud
Global sensitivity analysis (GSA) quantifies the influence of uncertain variables in a mathematical model. The Sobol' indices, a commonly used tool in GSA, seek to do this by attri…
Global Sensitivity Analysis of High Dimensional Neuroscience Models: An Example of Neurovascular Coupling
J. L. Hart, P. A. Gremaud, T. David
The complexity and size of state-of-the-art cell models have significantly increased in part due to the requirement that these models possess complex cellular functions which are t…
Robustness of the Sobol' indices to distributional uncertainty
Joseph Hart, Pierre Gremaud
Global sensitivity analysis (GSA) is used to quantify the influence of uncertain variables in a mathematical model. Prior to performing GSA, the user must specify (or implicitly as…
An approximation theoretic perspective of the Sobol' indices with dependent variables
Joseph Hart, Pierre Gremaud
The Sobol' indices are a recognized tool in global sensitivity analysis. When the uncertain variables in a model are statistically independent, the Sobol' indices may be easily int…
Global sensitivity analysis for statistical model parameters
Joseph Hart, Julie Bessac, Emil Constantinescu
Global sensitivity analysis (GSA) is frequently used to analyze the influence of uncertain parameters in mathematical models and simulations. In principle, tools from GSA may be ex…
Efficient computation of Sobol' indices for stochastic models
Joseph L. Hart, Alen Alexanderian, Pierre A. Gremaud
Stochastic models are necessary for the realistic description of an increasing number of applications. The ability to identify influential parameters and variables is critical to a…