Uncertainty Bounds for Multivariate Machine Learning Predictions on High-Strain Brittle Fracture
This work addresses the problem of computationally expensive simulations for brittle fracture by providing a faster machine learning emulator with quantified uncertainty, which is important for engineers and material scientists.
The authors developed a machine learning emulator to accelerate the simulation of crack network evolution in brittle materials under high strain rate impact, a process that is computationally intensive. They extended heteroscedastic uncertainty estimates to bound the predictions of this multiple-output emulator, finding that the predictions were accurate within the estimated errors, though the uncertainty estimates were somewhat conservative.
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.