# Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations

@article{Sunseri2020HyperdifferentialSA, title={Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations}, author={Isaac Sunseri and Joseph L. Hart and Bart G. van Bloemen Waanders and Alen Alexanderian}, journal={Inverse Problems}, year={2020}, volume={36} }

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 determined directly, but rather is estimated using (typically sparse and noisy) measurements of the states. The data is usually not sufficient to simultaneously inform all of the parameters. Consequently, the governing model typically contains parameters which are uncertain but must be specified for a complete model…

## 14 Citations

### Hyper-differential sensitivity analysis for nonlinear Bayesian inverse problems

- Mathematics, Computer ScienceArXiv
- 2022

This work focuses on analyzing the sensitivity of the MAP point and the Bayes risk and makes full use of the information embedded in the Bayesian inverse problem to establish a mathematical framework and a detailed computational approach for computing the proposed HDSA indices.

### Optimal Design of Validation Experiments for the Prediction of Quantities of Interest

- Computer Science
- 2023

This paper addresses two specific issues arising when designing validation experiments, including determining an appropriate validation scenario in cases where the prediction scenario cannot be carried out in a controlled environment and the selection of observations when the quantity of interest cannot be readily observed.

### A new perspective on parameter study of optimization problems

- MathematicsAppl. Math. Lett.
- 2023

We provide a new perspective on the study of parameterized optimization problems. Our approach combines methods for post-optimal sensitivity analysis and ordinary differential equations to quantify…

### Sensitivity-Driven Experimental Design to Facilitate Control of Dynamical Systems

- MathematicsJournal of Optimization Theory and Applications
- 2023

Control of nonlinear dynamical systems is a complex and multifaceted process. Essential elements of many engineering systems include high-fidelity physics-based modeling, offline trajectory planning,…

### Hyper-differential sensitivity analysis in the context of Bayesian inference applied to ice-sheet problems

- Mathematics
- 2022

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### Adaptive Basis Sets for Practical Quantum Computing

- Chemistry
- 2022

Electronic structure calculations on small systems such as H 2 , H 2 O, LiH, and BeH 2 with chemical accuracy are still a challenge for the current generation of the noisy intermediate-scale quantum…

### Hyper-differential sensitivity analysis with respect to model discrepancy: Calibration and optimal solution updating

- Computer ScienceArXiv
- 2022

This article introduces a novel approach which uses limited high-ﬁdelity data to calibrate the model discrepancy in a Bayesian framework and propagate it through the optimization problem, providing both an improvement in the optimal solution and a characterization of uncertainty due to the limited accessibility of high- ﬁDelity data.

### Hyper-differential sensitivity analysis with respect to model discrepancy: mathematics and computation

- Mathematics, Computer ScienceArXiv
- 2022

A general representation of the discrepancy is introduced and a proposed framework is presented which combines the PDE discretization, post-optimality sensitivity operator, adjoint-based derivatives, and a randomized generalized singular value decomposition to enable scalable computation.

### Hyper-differential sensitivity analysis for inverse problems governed by ODEs with application to COVID-19 modeling

- MathematicsMathematical biosciences
- 2022

### Enabling and interpreting hyper-differential sensitivity analysis for Bayesian inverse problems

- MathematicsArXiv
- 2021

This article proposes using hyper-differential sensitivity analysis (HDSA) to assess the sensitivity of the maximum a posteriori probability (MAP) and the Laplace approximation of the posterior covariance to changes in the auxiliary parameters.

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