Expert-informed neural network (EINN) for the forming depth prediction from a small-scale sheet metal forming database

It is well established that supervised machine learning (SML) models often perform poorly when presented with new inputs outside their latent space, due to misalignment with the features learned during the training process. Although Physics-Informed Neural Networks (PINNs) have demonstrated promising results, their reliance on physics-based partial differential equations (PDEs) limits their applicability in manufacturing engineering, where PDEs are not easily definable. To overcome this challenge, this work introduces an Expert-Informed Neural Network (EINN), where PDEs are numerically derived based on engineering expertise and incorporated into the backpropagation scheme to enhance extrapolation accuracy. To evaluate the EINN architecture, a dataset comprising 15 finite element analyses (FEA) and 9 cold-warm stamping experiments on 0.1 mm thick pure titanium (Ti) sheets was employed. The EINN was benchmarked against two SML models, Extreme Gradient Boosting (XGB) and Deep Neural Networks (DNN) demonstrating similar training and validation scores with both benchmark models while outperforming them in predicting the forming depth limit in more complex scenarios beyond its original latent space, achieving an average accuracy improvement of over 25%.