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Exploring Various Sequential Learning Methods for Deformation History Modeling

Muhammed Adil Yatkin, Mihkel Korgesaar, Jani Romanoff, Umit Islak, Hasan Kurban

TL;DR

The paper addresses the challenge of predicting deformation localization under bilinear loading by learning deformation history with three NN architectures: 1D CNN, encoder-decoder RNN (GRU-based), and Transformer. Using bilinear loading histories generated from MK-FE simulations, the study finds that encoder-decoder RNNs achieve the lowest training and test error, but their outputs vary with history truncation, violating the physical requirement that current damage states $D^t$ depend deterministically on past history. Transformers exhibit strong, stable convergence and consistent predictions, while 1D-CNNs perform poorly. The results highlight a critical mismatch between certain architectural dynamics and physical state evolution, guiding surrogate-model design for FE simulations and underscoring the importance of physical-consistency in history-dependent modeling; the dataset used is publicly available for replication.

Abstract

Current neural network (NN) models can learn patterns from data points with historical dependence. Specifically, in natural language processing (NLP), sequential learning has transitioned from recurrence-based architectures to transformer-based architectures. However, it is unknown which NN architectures will perform the best on datasets containing deformation history due to mechanical loading. Thus, this study ascertains the appropriateness of 1D-convolutional, recurrent, and transformer-based architectures for predicting deformation localization based on the earlier states in the form of deformation history. Following this investigation, the crucial incompatibility issues between the mathematical computation of the prediction process in the best-performing NN architectures and the actual values derived from the natural physical properties of the deformation paths are examined in detail.

Exploring Various Sequential Learning Methods for Deformation History Modeling

TL;DR

The paper addresses the challenge of predicting deformation localization under bilinear loading by learning deformation history with three NN architectures: 1D CNN, encoder-decoder RNN (GRU-based), and Transformer. Using bilinear loading histories generated from MK-FE simulations, the study finds that encoder-decoder RNNs achieve the lowest training and test error, but their outputs vary with history truncation, violating the physical requirement that current damage states depend deterministically on past history. Transformers exhibit strong, stable convergence and consistent predictions, while 1D-CNNs perform poorly. The results highlight a critical mismatch between certain architectural dynamics and physical state evolution, guiding surrogate-model design for FE simulations and underscoring the importance of physical-consistency in history-dependent modeling; the dataset used is publicly available for replication.

Abstract

Current neural network (NN) models can learn patterns from data points with historical dependence. Specifically, in natural language processing (NLP), sequential learning has transitioned from recurrence-based architectures to transformer-based architectures. However, it is unknown which NN architectures will perform the best on datasets containing deformation history due to mechanical loading. Thus, this study ascertains the appropriateness of 1D-convolutional, recurrent, and transformer-based architectures for predicting deformation localization based on the earlier states in the form of deformation history. Following this investigation, the crucial incompatibility issues between the mathematical computation of the prediction process in the best-performing NN architectures and the actual values derived from the natural physical properties of the deformation paths are examined in detail.

Paper Structure

This paper contains 13 sections, 5 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Machine Learning Methods
  3. Prior Work
  4. Neural Network architectures for history dependent damage
  5. Sequential Learning Approaches
  6. Recurrent Neural Networks
  7. Convolutional Networks
  8. Transformers
  9. Discussion of the Results
  10. Incompatibility of Encoder-Decoder RNNs with physical state
  11. Conclusions
  12. Acknowledgements
  13. Data availability

Figures (9)

  • Figure 1: The mapping defined in Yatkin and Kõrgesaar Yatkin2024 from bilinear strain paths to the damage indicator D.
  • Figure 2: While the encoder part generates the final hidden state, the decoder part uses it as an initial hidden state and calculates the outputs.
  • Figure 3: Two layered recurrent neural network (RNN) architecture
  • Figure 4: Comparison results between 1D-CNN, RNNs, and Transformers based NN architectures on the learning of bilinear deformation history paths.
  • Figure 5: RNN architecture training results on the bilinear loading paths
  • ...and 4 more figures