# Adaptive Strategies For Efficient Model Reduction In High-Dimensional Inverse Problems

## TL;DR

This paper introduces an adaptive, differentiable PCA-based method for efficient model reduction in high-dimensional inverse problems, enhancing optimization processes like history matching.

## Contribution

It presents a novel adaptive PCA-based parametrization technique that adjusts based on objective function behavior, improving model reduction in large-scale inverse problems.

## Key findings

- Enables efficient model reduction in high-dimensional inverse problems.
- Compatible with gradient-based optimization algorithms.
- Improves accuracy of history matching processes.

## Abstract

This work explores a novel approach for adaptive, differentiable parametrization of large-scale non-stationary random fields. Coupled with any gradient-based algorithm, the method can be applied to variety of optimization problems, including history matching. The developed technique is based on principal component analysis (PCA), but, in contrast to other PCA-based methods, allows to amend parametrization process regarding objective function behaviour.