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Learning latent hardening: enhancing deep learning with domain knowledge for material inverse problems.

Qinyi Tian1, Winston Lindqwister2, Manolis Veveakis1

  • 1Department of Civil and Environmental Engineering, Duke University, Durham, NC, USA.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|September 25, 2025
PubMed
Summary

Incorporating domain knowledge into deep learning models significantly improves their predictive performance in data-scarce materials science inverse problems. This approach enhances feature selection and recognizes crucial links between material behavior and microstructure.

Keywords:
deep learninginverse problemmachine learningmicrostructuresporous materials

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Area of Science:

  • Materials Science
  • Computational Materials Science
  • Applied Mathematics

Background:

  • Deep learning (DL) and machine learning (ML) excel at modeling complex relationships but often require large datasets.
  • Data scarcity is a significant challenge in many materials science inverse problems.
  • Domain-specific knowledge can potentially enhance the performance of DL/ML models in data-limited scenarios.

Purpose of the Study:

  • To investigate the impact of incorporating domain-specific knowledge of mechanical behavior on the predictive performance of DL/ML models in data-scarce inverse problems.
  • To propose and evaluate a novel two-step framework, learning latent hardening (LLH), for materials science inverse problems.
  • To compare the effectiveness of various DL and ML models with and without domain knowledge integration.

Main Methods:

  • A two-step framework, learning latent hardening (LLH), was developed.
  • The first step uses a deep neural network (DNN) to reconstruct full stress-strain curves from partial data, capturing latent mechanical responses based on microstructural features.
  • The second step leverages reconstructed curves to predict key microstructural features of porous materials. Six models (CNNs, DNN, XGBoost, KNN, LSTM, RF) were trained with and without domain knowledge.

Main Results:

  • Models incorporating domain-specific mechanical knowledge consistently achieved higher performance metrics ([Formula: see text] values).
  • Without domain knowledge, models failed to recognize the link between stress-strain behavior and microstructural changes.
  • Models enhanced with domain knowledge demonstrated superior feature selection, identifying critical stress-strain characteristics for microstructure prediction.

Conclusions:

  • Domain-specific knowledge plays a critical role in guiding deep learning models, especially in data-scarce environments.
  • Combining domain expertise with data-driven approaches is essential for reliable and accurate outcomes in materials science.
  • The proposed LLH framework effectively leverages domain knowledge to improve predictive accuracy in materials inverse problems.