# Accelerated scale bridging with sparsely approximated Gaussian learning

## TL;DR

This paper introduces a hierarchical sparse Gaussian process regression method that significantly reduces computational costs and errors in multiscale modeling, enabling more efficient simulations of complex systems.

## Contribution

The paper develops a novel sparse Gaussian process regression approach using hierarchical sparse Cholesky decomposition for multiscale modeling.

## Key findings

- Substantial reduction in computational cost.
- Lower solution error compared to previous methods.
- Effective approximation of the equation of state in multiscale models.

## Abstract

Multiscale modeling is a systematic approach to describe the behavior of complex systems by coupling models from different scales. The approach has been demonstrated to be very effective in areas of science as diverse as materials science, climate modeling and chemistry. However, routine use of multiscale simulations is often hindered by the very high cost of individual at-scale models. Approaches aiming to alleviate that cost by means of Gaussian process regression based surrogate models have been proposed. Yet, many of these surrogate models are expensive to construct, especially when the number of data needed is large. In this article, we employ a hierarchical sparse Cholesky decomposition to develop a sparse Gaussian process regression method and apply the method to approximate the equation of state of an energetic material in a multiscale model of dynamic deformation. We demonstrate that the method provides a substantial reduction both in computational cost and solution error as compared with previous methods.