A novel approach for Tool-Narayanaswamy-Moynihan model parameter extraction using multi-scale neural model

The accurate determination of parameters in the Tool-Narayanaswamy-Moynihan (TNM) model, which describes the viscoelastic behavior of glass-forming materials, is crucial for predicting material responses through various thermal histories. Traditional methods rely heavily on curve-fitting techniques; however, these often fail due to noise in the data. Furthermore, traditional methods are computationally intensive and prone to inaccuracies, particularly when dealing with complex datasets or when the initial parameter guesses are far from optimal; also, they require a skilled personnel.

In this study, we propose the application of a multi-scale convolutional neural network (MCNN) as a machine learning approach to address these challenges. The MCNN model is trained on a comprehensive simulated dataset encompassing a wide range of TNM parameters, allowing it to learn intricate patterns and dependencies within the data that are difficult to capture with conventional methods. Our results show that the MCNN significantly improves the accuracy of the parameter estimations for $\beta$ and $x$ across the entire spectrum of tested conditions, achieving performance that is not only comparable to, but often surpasses, traditional curve-fitting methods. Furthermore, the MCNN demonstrates superior robustness when initial parameter estimates are suboptimal or when the dataset exhibits significant noise. Although the prediction accuracy for the activation energy $\Delta h^{\ast }$ and the pre-exponential factor $log\left(A\right)$ was somewhat lower, the method still provides valuable estimates that can be refined with supplementary techniques.

This work highlights the potential of machine learning approaches like MCNN to revolutionize the parameter extraction process in complex physical models, reducing the reliance on manual curve-fitting and providing a more automated, scalable solution. We also analyze the primary sources of prediction errors in the MCNN outputs and offer insights into future improvements, including model architecture refinements and the integration of additional physical constraints. Our findings suggest that this approach can be extended to other domains where similar models are employed, paving the way for broader applications of machine learning in materials science.