What does this research mean for the field?

A single-task machine learning model trained solely on experimental data and explicitly including indentation load outperforms models incorporating DFT-computed data for accurate material hardness prediction. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to develop machine learning models for predicting load-dependent hardness of materials more accurately.

July 17, 2026Applied Physics A0 citationsOpen Access

Load-dependent hardness prediction for materials using machine learning

MMMadhubanti MukherjeeGeorgia Institute of Technology RRRampi RamprasadGeorgia Institute of Technology HSHarikrishna SahuGeorgia Institute of Technology

Key Points

The aim is to develop machine learning models for predicting load-dependent hardness of materials more accurately.
Developed machine learning models using a curated dataset of load-dependent Vickers hardness measurements.
Compared single-task and multi-task models for predicting hardness.
Evaluated model performance through root mean squared error (RMSE) and coefficient of determination (R2) across training and testing data.
Single-task Gaussian Process Regression model showed a RMSE range of 2.73-2.90/3.16-3.91 GPa and R2 values between 0.96-0.95/0.94-0.91.
Moderate correlation between DFT-based and experimental Vickers hardness values was noted.
Explicit inclusion of indentation load led to higher accuracy in hardness predictions compared to other methods.

Abstract

Abstract Superhard materials are critical for wear-resistant and high-stress applications. Conventional approaches correlating hardness with elastic moduli derived from DFT calculations enable rapid screening but overlook the strong load dependence of hardness. In this work, machine learning (ML) models were developed using a large, curated dataset of load-dependent experimental Vickers hardness (H ᵥ) measurements. Moderate correlation was observed between experimental and DFT-based H ᵥ values, whereas a single-task ML model trained solely on experimental data outperformed multi-task models that combined experimental and computed data. The superior performance of the single-task model highlights that explicit inclusion of indentation load, along with compositional, electronic, and structural descriptors, is essential and sufficient for accurate hardness prediction, beyond what can be achieved using DFT-accessible bulk and shear moduli alone (or in tandem with experimental data). Specifically, the single-task Gaussian Process Regression (GPR) yields a train-test root mean squared error (RMSE) in a range of 2. 73-2. 90/3. 16-3. 91 GPa and R² in a range of 0. 96-0. 95/0. 94-0. 91 across five random splits of train and test sets. These results emphasize the importance of high-quality experimental data and explicit inclusion of measurement conditions, particularly load, in the development of reliable hardness prediction models.

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