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

Abstract:

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.

• Periodical: Key Engineering Materials (Volume 1049)
• Pages: 13-28
• DOI: https://doi.org/10.4028/p-B4tPZr
• Online since: April 2026
• Authors: Luca Quagliato*, Johannes Seitz, Mattia Perin, Dominik Malejka, Tobias Moser, Caterina Zanella, Bernd Kuhlenkötter
• Keywords: Forces Modeling, Gematrical Modeling, Proxy-Physics Informed Neural Networks (P-PINNs), Radial-Axial Ring Rolling (RARR), Transfer Learning

References

[1] J. Seitz, Q. Wang, L. Goldbach, T. Moser, A. Brosius, B. Kuhlenkötter. A Review of Data-Centric Optimization and Machine Learning in Ring Rolling, in: Drossel, WG., Ihlenfeldt, S., Dix, M. (eds) Production at the Leading Edge of Technology. WGP 2024. Lecture Notes in Production Engineering. Springer, Cham, 2025, pp.242-252.

DOI: 10.1007/978-3-031-86893-1_27

[2] J.M. Allwood, A.E. Tekkaya, T.F. Stanistreet, The development of ring rolling technology, Steel Res. Int. 76 (2005) 111-120.

DOI: 10.1002/srin.200505981

[3] J.B. Hawkyard, W. Johnson, J. Kirkland, E. Appleton, Analyses for roll force and torque in ring rolling, with some supporting experiments, Int. J. Mech. Sc. 15 (1973) 873–893.

DOI: 10.1016/0020-7403(73)90018-0

[4] A.G. Mamalis, W. Johnson, J.B. Hawkyard, Pressure distribution, roll force and torque in cold ring rolling, J. Mech. Eng. Sc. 18 (1976) 196-204.

DOI: 10.1243/jmes_jour_1976_018_033_02

[5] L. Quagliato, G.A. Berti, D. Kim, N. Kim, Slip line model for forces estimation in the radial–axial ring rolling process, Int. J. Mech. Sc. 138–139 (2018) 17-33.

DOI: 10.1016/j.ijmecsci.2018.01.025

[6] G.A. Berti, L. Quagliato, M. Monti, Set-up of radial–axial ring-rolling process: Process worksheet and ring geometry expansion prediction, Int. J. Mech. Sc. 99 (2015) 58–71.

DOI: 10.1016/j.ijmecsci.2015.05.004

[7] L. Guo, H. Yang, Towards a steady forming condition for radial–axial ring rolling, Int. J. Mech. Sc. 53 (2011) 286–299.

DOI: 10.1016/j.ijmecsci.2011.01.010

[8] N. Kim, H. Kim, K. Jin, Optimal design to reduce the maximum load in ring rolling process, Int. J. Prec. Eng. Manuf. 13 (2012) 1821–1828.

DOI: 10.1007/s12541-012-0239-4

[9] Z.W. Wang, J.P. Fan, D.P. Hu, C.Y. Tang, C.P. Tsui, Complete modeling and parameter optimization for virtual ring rolling, Int. J. Mech. Sc. 52 (2010) 1325-1333.

DOI: 10.1016/j.ijmecsci.2010.06.008

[10] J. Cao, M. Bambach, M. Merklein, M. Mozaffar, T. Xue, Artificial intelligence in metal forming, CIRP Annals – Manuf. Tech. (2024) 1–27.

DOI: 10.1016/j.cirp.2024.04.102

[11] L. Quagliato, J. Seitz, M. Perin, Machine learning modeling for material science and manufacturing: overview and perspectives for the future, AI Mater. (2025) 0005.

DOI: 10.55092/20250005

[12] A. Parvizi, H.R.R. Raftar, Application of artificial neural network and genetic algorithm to predict and optimize load and torque in T-section profile ring rolling, Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sc. 233 (2019) 5966–5976.

DOI: 10.1177/0954406219861989

[13] I. Mirandola, G.A. Berti, R. Caracciolo, S. Lee, N. Kim, L. Quagliato, Machine learning-based models for the estimation of the energy consumption in metal forming processes, Metals 11 (2021) 833.

DOI: 10.3390/met11050833

[14] S. Lee, Y. Lim, L. Galdos, T. Lee, L. Quagliato, Gaussian process regression-driven deep drawing blank design method, Int. J. Mech. Sc. 265 (2024) 108898.

DOI: 10.1016/j.ijmecsci.2023.108898

[15] S. Lee, J. Park, N. Kim, T. Lee, L. Quagliato, Extreme gradient boosting-inspired process optimization algorithm for manufacturing engineering applications, Mat. & Des. 226 (2023) 111625.

DOI: 10.1016/j.matdes.2023.111625

[16] V. Modanloo, S. Jang, T. Lee, L. Quagliato, Gradient enhanced-expert informed neural network (GE-EINN) for forming depth prediction from a small-scale metal stamping dataset, J. Manuf. Proc. 140 (2025) 224–240.

DOI: 10.1016/j.jmapro.2025.02.052

[17] R. Lafarge, S. Hütter, M. Tulke, T. Halle, A. Brosius, Data-based model predictive control for ring rolling, Prod. Eng. 15 (2021) 821–831.

DOI: 10.1007/s11740-021-01063-1

[18] S. Fahle, T. Glaser, A. Kneißler, B. Kuhlenkötter, Improving quality prediction in radial-axial ring rolling using a semi-supervised approach and generative adversarial networks for synthetic data generation, Prod. Eng. 16 (2022) 175–185.

DOI: 10.1007/s11740-021-01075-x

[19] C. Cappellini, C. Giardini, S. Bocchi, A multi-objective optimization workflow of ring-rolling process parameters based on production energy and time, Procedia CIRP 122 (2024) 683–688.

DOI: 10.1016/j.procir.2024.01.095

[20] J. Seitz, T. Moser, S. Fahle, C. Prinz, B. Kuhlenkötter, Transfer learning approaches in the domain of radial-axial ring rolling for machine learning applications, Proceedings of the 5th Conference on Production Systems and Logistics (CPSL) (2023).

DOI: 10.25368/2023.190

[21] L. Quagliato, S. Kim, O.R. Hassan, T. Lee, Heel pad's hyperelastic properties and gait parameters reciprocal modelling by a Gaussian mixture model and extreme gradient boosting framework, Biomedical Signal Processing and Control 107 (2025) 107818.

DOI: 10.1016/j.bspc.2025.107818

[22] V. Modanloo, M. Elyasi, T. Lee, L. Quagliato, Modeling of tensile strength and wear resistance in friction stir processed MMCs by metaheuristic optimization and supervised learning, The International Journal of Advanced Manufacturing Technology (2025).

DOI: 10.1007/s00170-025-16070-0

[23] S. Cuomo, V. Schiano Di Cola, F. Giampaolo, G. Rozza, M. Raissi, F. Piccialli, Scientific machine learning through physics-informed neural networks: Where we are and what's next, Journal of Scientific Computing 92 (2022) 88.

DOI: 10.1007/s10915-022-01939-z

[24] A. Deng, X. Li, D. Hu, T. Wang, H. Xiong, C.-Z. Xu, Towards inadequately pre-trained models in transfer learning, in: Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2023, p.19397–19406.

DOI: 10.1109/iccv51070.2023.01777

[25] J.M. Springer, S. Goyal, K. Wen, T. Kumar, X. Yue, S. Malladi, G. Neubig, A. Raghunathan, Overtrained language models are harder to fine-tune, arXiv preprint arXiv:2503.19206, 2025.