Robotics · 2026-10-16
Thermodynamically Consistent Machine Learning for Fracture Prediction in Heterogeneous Materials
Muhamad Alim, Xiaolong He, Mei-Na Tsao, Chi-Hua Yu, J. S. Chen
AI-assisted summary based on the paper. Consult the linked source for methods and limitations. Benchmark numbers appear after editor verification.
TL;DR
The authors introduce tLaSDI-pGFINNs to predict fracture patterns and evolution in heterogeneous materials. The model learns a thermodynamic state in a low-dimensional latent space using parametric GENERIC Formalism-Informed Neural Networks (pGFINNs), enforcing total energy conservation and non-decreasing entropy generation via hard constraints. A geometry-conditioned autoencoder improves geometry-guided learning; experiments show better fracture-pattern accuracy than an AE-LSTM baseline and thermodynamic constraint preservation on unseen samples.
Why it matters
Fracture evolution prediction is typically computationally expensive and many ML fracture models act as black boxes or require large datasets. By embedding thermodynamic principles directly into the neural architecture (GENERIC structure in latent dynamics) and adding geometry conditioning, the approach aims to improve physical consistency and generalization for unseen fracture evolutions in heterogeneous materials.
Method
- Learn fracture evolution in a low-dimensional latent space using tLaSDI-pGFINNs: a convolutional geometry-conditioned autoencoder encodes high-dimensional states and a pGFINN predicts thermodynamically consistent latent states.
- Enforce GENERIC thermodynamic principles by hard-constraint operator construction in pGFINNs, designed to satisfy symmetry and degeneracy conditions that imply energy conservation and non-decreasing entropy (via first and second laws).
- Train with a loss combining integration consistency (latent next-step vs. integrated pGFINN dynamics), reconstruction loss, Jacobian/Sobolev-type loss, and a regularization/modelling term; evaluate with autoregressive rollout on testing sets.
Limitation
The paper text does not state a specific limitation of the proposed method.
Abstract (from arXiv)
Understanding fracture behavior is critical for assessing the structural integrity and longevity. Highly time-consuming physics-based fracture simulations motivate the development of machine-learning-based fracture evolution prediction with surrogate models. However, most existing machine-learning models for fracture prediction operate as black boxes and require large training datasets to generalize reliably. In this work, Thermodynamically Consistent Latent Dynamics Identification (tLaSDI) for parametric systems is introduced to predict fracture patterns and evolution in heterogeneous materials. The model learns the thermodynamic state variable in a lower-dimensional latent space using parametric GENERIC Formalism-Informed Neural Networks (pGFINNs) that enforce key thermodynamic principles, such as total energy conservation and entropy generation. This model embeds physics into the neural network architecture using a hard-constraint method that inherently complies with the underlying thermodynamic principles. The proposed tLaSDI-pGFINNs is further enhanced by a Geometry-Conditioned Autoencoder in learning the geometry configuration for effective geometry-guided learning. The energy and entropy evolution histories demonstrate that the model preserves the thermodynamic constraints on unseen testing samples. The results further show that tLaSDI-pGFINNs can more accurately capture both fracture patterns and the subsequent fracture evolution than the purely data-driven Autoencoder Long Short-Term Memory (AE-LSTM) model.
Related papers
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Publication record
Bibliographic evidence describes where and when a record appeared. It does not validate scientific claims.
First public release: 2026-07-12 · Indexed by Pub-AI: 2026-10-16 UTC
Thermodynamically Consistent Machine Learning for Fracture Prediction in Heterogeneous Materials
Preprint posted: 2026-07-12 · Original record ↗
- arxiv
- 2610.20614
Explicit source versions (1)
- v1 · 2026-07-12
- Preprint available
Source date: 2026-07-12 · First detected: 2026-10-25 UTC · Historical baseline
Source evidence (1)
- Official evidence ↗ · atom:published (official metadata)
Abstract · arxiv
Understanding fracture behavior is critical for assessing the structural integrity and longevity. Highly time-consuming physics-based fracture simulations motivate the development of machine-learning-based fracture evolution prediction with surrogate models. However, most existing machine-learning models for fracture prediction operate as black boxes and require large training datasets to generalize reliably. In this work, Thermodynamically Consistent Latent Dynamics Identification (tLaSDI) for parametric systems is introduced to predict fracture patterns and evolution in heterogeneous materials. The model learns the thermodynamic state variable in a lower-dimensional latent space using parametric GENERIC Formalism-Informed Neural Networks (pGFINNs) that enforce key thermodynamic principles, such as total energy conservation and entropy generation. This model embeds physics into the neural network architecture using a hard-constraint method that inherently complies with the underlying thermodynamic principles. The proposed tLaSDI-pGFINNs is further enhanced by a Geometry-Conditioned Autoencoder in learning the geometry configuration for effective geometry-guided learning. The energy and entropy evolution histories demonstrate that the model preserves the thermodynamic constraints on unseen testing samples. The results further show that tLaSDI-pGFINNs can more accurately capture both fracture patterns and the subsequent fracture evolution than the purely data-driven Autoencoder Long Short-Term Memory (AE-LSTM) model.