9 papers
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…
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…