Proxy-Physics-Informed and Transfer Learning Networks for Radial-Axial Ring Rolling (RARR) under Varying Data Availability

This contribution presents a proof-of-concept and benchmark analysis between two different approaches for multiple domain modeling, employing numerical and experimental results relevant to the Radial-Axial Ring Rolling (RARR). First, a finite element method (FEM) simulation data-based Deep Neural Network (DNN) was employed as base model for a subsequent transfer learning (TL), carried out by employing 40 experimental (EXP) data belonging to a different RARR domain. The DNN-TL model is benchmarked against the proposed solution, in terms of a Proxy-Physics Informed Neural Network (P-PINN), defined using proxy equations for the outer diameter (OD) expansion, the radial force (RF), and the axial force (AF) and trained on 30 FEM and 30 EXP data. The proxy equations for the P-PINN are based on known knowledge and analytical formulations developed for the RARR. The results show that employing the whole 218 cases strong FEM database for the training of the base DNN model results in high prediction accuracy on the FEM cases and can be adapted well through TL. When employing only 30 FEM cases for the training of the base DNN model results in slight improvements for RF and in a significant drop of performance for AF, after TL. Instead, in a limited data scenario, the P-PINN model, powered equally by data and proxy equations steering the learning process, is capable of modeling well and simultaneously both FEM and EXP cases with reasonable accuracy, averaging at 3.7% for OD and 24.0% for RF/AF.