LaDEEP: A Deep Learning-based Surrogate Model for Large Deformation of Elastic-Plastic Solids

TL;DR

LaDEEP is a Transformer-based deep learning surrogate model that accurately and efficiently predicts large elastic-plastic deformations, significantly outperforming traditional methods and previous models in speed and accuracy, with successful industrial deployment.

Contribution

This work introduces LaDEEP, a novel deep learning model tailored for elastic-plastic solid deformation, incorporating sequence encoding and a two-stage Transformer to handle complex physical processes.

Findings

LaDEEP is five times faster than finite element methods with similar accuracy.

It achieves a 20.47% improvement over existing deep learning baselines.

The model performs well in real-world industrial applications.

Abstract

Scientific computing for large deformation of elastic-plastic solids is critical for numerous real-world applications. Classical numerical solvers rely primarily on local discrete linear approximation and are constrained by an inherent trade-off between accuracy and efficiency. Recently, deep learning models have achieved impressive progress in solving the continuum mechanism. While previous models have explored various architectures and constructed coefficient-solution mappings, they are designed for general instances without considering specific problem properties and hard to accurately handle with complex elastic-plastic solids involving contact, loading and unloading. In this work, we take stretch bending, a popular metal fabrication technique, as our case study and introduce LaDEEP, a deep learning-based surrogate model for \textbf{La}rge \textbf{De}formation of \textbf{E}lastic-\textbf{P}lastic Solids. We encode the partitioned regions of the involved slender solids into a token sequence to maintain their essential order property. To characterize the physical process of the solid deformation, a two-stage Transformer-based module is designed to predict the deformation with the sequence of tokens as input. Empirically, LaDEEP achieves five magnitudes faster speed than finite element methods with a comparable accuracy, and gains 20.47\% relative improvement on average compared to other deep learning baselines. We have also deployed our model into a real-world industrial production system, and it has shown remarkable performance in both accuracy and efficiency.