Investigating Deep Learning Model Calibration for Classification Problems in Mechanics

TL;DR

This paper investigates the calibration of deep learning models in engineering mechanics, evaluating methods like ensemble averaging and temperature scaling across diverse datasets to improve probability accuracy.

Contribution

It provides a comprehensive analysis of model calibration techniques in mechanics-related deep learning applications, highlighting ensemble averaging as particularly effective.

Findings

Ensemble averaging improves model calibration consistently.

Temperature scaling offers limited calibration benefits.

The study covers seven diverse mechanics datasets.

Abstract

Recently, there has been a growing interest in applying machine learning methods to problems in engineering mechanics. In particular, there has been significant interest in applying deep learning techniques to predicting the mechanical behavior of heterogeneous materials and structures. Researchers have shown that deep learning methods are able to effectively predict mechanical behavior with low error for systems ranging from engineered composites, to geometrically complex metamaterials, to heterogeneous biological tissue. However, there has been comparatively little attention paid to deep learning model calibration, i.e., the match between predicted probabilities of outcomes and the true probabilities of outcomes. In this work, we perform a comprehensive investigation into ML model calibration across seven open access engineering mechanics datasets that cover three distinct types of mechanical problems. Specifically, we evaluate both model and model calibration error for multiple machine learning methods, and investigate the influence of ensemble averaging and post hoc model calibration via temperature scaling. Overall, we find that ensemble averaging of deep neural networks is both an effective and consistent tool for improving model calibration, while temperature scaling has comparatively limited benefits. Looking forward, we anticipate that this investigation will lay the foundation for future work in developing mechanics specific approaches to deep learning model calibration.