# Allocation strategies for high fidelity models in the multifidelity regime

## TL;DR

This paper introduces a novel resource allocation method for high fidelity models in multifidelity simulations, using a regularized group lasso approach to improve subset selection and performance.

## Contribution

It formulates the allocation problem as a regularized subset selection task solved via group lasso, providing a new approach for resource distribution in multifidelity modeling.

## Key findings

- Group lasso-based allocation outperforms classical and machine learning methods.
- The approach is effective on synthetic and real-world problems.
- Regularization enables efficient subset selection for expensive simulations.

## Abstract

We propose a novel approach to allocating resources for expensive simulations of high fidelity models when used in a multifidelity framework. Allocation decisions that distribute computational resources across several simulation models become extremely important in situations where only a small number of expensive high fidelity simulations can be run. We identify this allocation decision as a problem in optimal subset selection, and subsequently regularize this problem so that solutions can be computed. Our regularized formulation yields a type of group lasso problem that has been studied in the literature to accomplish subset selection. Our numerical results compare performance of algorithms that solve the group lasso problem for algorithmic allocation against a variety of other strategies, including those based on classical linear algebraic pivoting routines and those derived from more modern machine learning-based methods. We demonstrate on well known synthetic problems and more difficult real-world simulations that this group lasso solution to the relaxed optimal subset selection problem performs better than the alternatives.