tLaSDI-pGFINNs embeds thermodynamic constraints in latent space to outperform AE-LSTM on fracture evolution in heterogeneous solids

The method combines a geometry-conditioned autoencoder with parametric GENERIC-informed neural networks that hard-constrain energy conservation and entropy production during training. On test samples the model maintains non-negative entropy generation and bounded total energy drift below 0.5 percent, while AE-LSTM baselines violate both constraints within the first 20 time steps. Fracture pattern Dice scores improve from 0.71 to 0.89 and crack-tip velocity error drops by 37 percent across 120 parametric simulations of random inclusion fields.

Existing surrogate models for fracture treat the network as a black box and require thousands of high-fidelity runs; tLaSDI reduces the data requirement by embedding the GENERIC structure directly in the architecture. This addresses a core limitation noted in prior physics-informed neural network literature on damage mechanics, where soft penalties often allow thermodynamic drift on extrapolation. The geometry-conditioned encoder further conditions the latent dynamics on explicit inclusion maps, enabling zero-shot transfer to new microstructures without retraining.

The approach connects to ongoing efforts in digital twins for aerospace composites and nuclear components, where reliable long-horizon fracture forecasts under variable loads remain a bottleneck. By guaranteeing thermodynamic consistency, tLaSDI outputs can be directly coupled to continuum damage models without post-hoc correction steps that currently dominate industrial workflows.

Next steps include extension to three-dimensional polycrystals and experimental calibration against in-situ tomography datasets; the authors flag that current results are limited to two-dimensional plane-strain cases with linear elastic constituents.