Uncertainty Bounds for Multivariate Machine Learning Predictions on High-Strain Brittle Fracture

TL;DR

This paper develops a method to estimate uncertainty bounds for multivariate machine learning models predicting crack evolution in brittle materials, enabling faster simulations with quantifiable error margins.

Contribution

It extends heteroscedastic uncertainty estimation to multivariate emulators, providing conservative error bounds for crack network evolution predictions.

Findings

Predictions are accurate within estimated errors.

Uncertainty estimates are somewhat conservative.

Method improves simulation efficiency with quantifiable confidence.

Abstract

Simulation of the crack network evolution on high strain rate impact experiments performed in brittle materials is very compute-intensive. The cost increases even more if multiple simulations are needed to account for the randomness in crack length, location, and orientation, which is inherently found in real-world materials. Constructing a machine learning emulator can make the process faster by orders of magnitude. There has been little work, however, on assessing the error associated with their predictions. Estimating these errors is imperative for meaningful overall uncertainty quantification. In this work, we extend the heteroscedastic uncertainty estimates to bound a multiple output machine learning emulator. We find that the response prediction is accurate within its predicted errors, but with a somewhat conservative estimate of uncertainty.