Explainable Machine Learning for Predicting Steel Toughness Using Multitask Sparse Neural Networks and CALPHAD Augmentation

Author(s):

B. Christopher Rinderspacher, Benjamin Szajewski, Heather Murdoch, and Gregory Barber

Abstract:

Neural networks model complex relationships found in data, including uncertainty. However, they traditionally function as “black boxes,” without providing mechanistic explanations for their predictions. This report presents a systematic evaluation of a novel method for training fully connected neural networks based on information-theoretic regularizations. These regularizations are designed to both sparsify the network structure and provide mechanistic insights into predictive computations. We applied this methodology to predict the Charpy V-Notch (CVN) and Izod impact toughness of steels. We compared models trained on composition-only inputs (20 variables) against those trained on inputs augmented with thermodynamic properties computed from CALPHAD (24 variables). We investigated the impact of three parameter p scheduling regimes—LinearScheduler, PiecewiseScheduler, and ExpScheduler—against a constant p baseline (no schedule). The empirical results show that enforcing information-theoretic regularizations does not degrade neural network performance; rather, when paired with appropriate schedules and CALPHAD augmentations, it yields highly sparsified networks with superior generalization. Specifically, the PiecewiseScheduler achieved the highest average network sparsification (≈ 84.36% pruned CVN sparsity, ≈ 83.81% pruned Izod sparsity), while the LinearScheduler combined with CALPHAD-augmented inputs produced the most accurate models, reaching a validation loss of 0.31 and high post-pruning R² values (R²_CVN = 0.73, R²_IZOD = 0.83).