# Physical Logic Enhanced Network for Small-Sample Bi-Layer Metallic Tubes Bending Springback Prediction

arXiv: https://arxiv.org/abs/2209.09870 · HTML: https://mlsanity.com/paper/2209.09870/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 18 references that are in the map.
- First posted on arXiv 20 Sep 2022.

## Builds on (most cited first, 2 of 2)

- [ERNIE: Enhanced Representation through Knowledge Integration](https://mlsanity.com/paper/1904.09223/) (2019)
- [Physics-Aware Gaussian Processes in Remote Sensing](https://mlsanity.com/paper/2012.07986/) (2020)

## Abstract (arXiv)

Bi-layer metallic tube (BMT) plays an extremely crucial role in engineering applications, with rotary draw bending (RDB) the high-precision bending processing can be achieved, however, the product will further springback. Due to the complex structure of BMT and the high cost of dataset acquisi-tion, the existing methods based on mechanism research and machine learn-ing cannot meet the engineering requirements of springback prediction. Based on the preliminary mechanism analysis, a physical logic enhanced network (PE-NET) is proposed. The architecture includes ES-NET which equivalent the BMT to the single-layer tube, and SP-NET for the final predic-tion of springback with sufficient single-layer tube samples. Specifically, in the first stage, with the theory-driven pre-exploration and the data-driven pretraining, the ES-NET and SP-NET are constructed, respectively. In the second stage, under the physical logic, the PE-NET is assembled by ES-NET and SP-NET and then fine-tuned with the small sample BMT dataset and composite loss function. The validity and stability of the proposed method are verified by the FE simulation dataset, the small-sample dataset BMT springback angle prediction is achieved, and the method potential in inter-pretability and engineering applications are demonstrated.