# Coupled Input-Output Dimension Reduction: Application to Goal-oriented Bayesian Experimental Design and Global Sensitivity Analysis

arXiv: https://arxiv.org/abs/2406.13425 · HTML: https://mlsanity.com/paper/2406.13425/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 64 references that are in the map.
- First posted on arXiv 19 Jun 2024.

## Builds on (most cited first, 18 of 18)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Model Reduction and Neural Networks for Parametric PDEs](https://mlsanity.com/paper/2005.03180/) (2020)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [Operator Learning: Algorithms and Analysis](https://mlsanity.com/paper/2402.15715/) (2024)
- [Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning](https://mlsanity.com/paper/2206.10745/) (2022)
- [Likelihood-informed dimension reduction for nonlinear inverse problems](https://mlsanity.com/paper/1403.4680/) (2014)
- [Certified dimension reduction in nonlinear Bayesian inverse problems](https://mlsanity.com/paper/1807.03712/) (2018)
- [Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems](https://mlsanity.com/paper/1802.06517/) (2018)
- [Large-scale Bayesian optimal experimental design with derivative-informed projected neural network](https://mlsanity.com/paper/2201.07925/) (2022)
- [A Fast and Scalable Method for A-Optimal Design of Experiments for Infinite-dimensional Bayesian Nonlinear Inverse Problems](https://mlsanity.com/paper/1410.5899/) (2014)
- [Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction](https://mlsanity.com/paper/1510.06053/) (2015)
- [Bayesian model calibration for block copolymer self-assembly: Likelihood-free inference and expected information gain computation via measure transport](https://mlsanity.com/paper/2206.11343/) (2022)
- [A layered multiple importance sampling scheme for focused optimal Bayesian experimental design](https://mlsanity.com/paper/1903.11187/) (2019)
- [Data-Free Likelihood-Informed Dimension Reduction of Bayesian Inverse Problems](https://mlsanity.com/paper/2102.13245/) (2021)
- [Tractable Optimal Experimental Design using Transport Maps](https://mlsanity.com/paper/2401.07971/) (2024)
- [Sensitivity analysis for multidimensional and functional outputs](https://mlsanity.com/paper/1311.1797/) (2013)
- [An efficient method for goal-oriented linear Bayesian optimal experimental design: Application to optimal sensor placemen](https://mlsanity.com/paper/2102.06627/) (2021)
- [A Greedy Sensor Selection Algorithm for Hyperparameterized Linear Bayesian Inverse Problems](https://mlsanity.com/paper/2301.12019/) (2023)

## Built on by (most cited first, 2 of 2)

- [Copula Active Subspaces I: A Score-Covariance Method for Reduced-Order Non-Gaussian Density Estimation](https://mlsanity.com/paper/2609.36142/) (2026)
- [Copula Active Subspaces II: Error Decomposition, A Posteriori Estimation, and Sharpness of the Bounds](https://mlsanity.com/paper/2610.14498/) (2026)

## Abstract (arXiv)

We introduce a new method to jointly reduce the dimension of the input and output space of a function between high-dimensional spaces. Choosing a reduced input subspace influences which output subspace is relevant and vice versa. Conventional methods focus on reducing either the input or output space, even though both are often reduced simultaneously in practice. Our coupled approach naturally supports goal-oriented dimension reduction, where either an input or output quantity of interest is prescribed. We consider, in particular, goal-oriented sensor placement and goal-oriented sensitivity analysis, which can be viewed as dimension reduction where the most important output or, respectively, input components are chosen. Both applications present difficult combinatorial optimization problems with expensive objectives such as the expected information gain and Sobol' indices. By optimizing gradient-based bounds, we can determine the most informative sensors and most influential parameters as the largest diagonal entries of some diagnostic matrices, thus bypassing the combinatorial optimization and objective evaluation.