A mesh-free multiresolution deep energy method with phase-field modeling of brittle fracture

arXiv:2608.24126 · cs.LG, cs.NA, math.NA · Submitted 2026-08-25 · Read on arXiv

cs.LG, cs.NA, math.NA

Submitted: 2026-08-25

Updated: 2026-08-25

Code: https://github.com/HannnZH/Meshfree-DEM-PhaseField

Terminology

• Regularization — 23× in this paper · explained in 3 episodes
• Benchmark — 16× in this paper · explained in 2 episodes
• Failure Modes — 6× in this paper · explained in 3 episodes
• Adam — 5× in this paper · explained in 2 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Activation Function — 3× in this paper · explained in 1 episode
• Core — 3× in this paper · explained in 2 episodes
• Decoupling — 3× in this paper · explained in 2 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Verification — 3× in this paper · explained in 2 episodes
• Adaptive Sampling — 2× in this paper · explained in 1 episode
• Embeddings — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Transfer Learning — 2× in this paper · explained in 10 episodes
• Abundance — 1× in this paper · explained in 1 episode
• Adaptation — 1× in this paper · explained in 1 episode
• Adaptivity — 1× in this paper · explained in 1 episode
• Admissibility — 1× in this paper · explained in 2 episodes
• Alternating Minimization — 1× in this paper · explained in 1 episode
• Benchmarking — 1× in this paper · explained in 4 episodes
• Calibration — 1× in this paper · explained in 7 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• DeepONet — 1× in this paper · explained in 2 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes

Sources

• Variational energy based XPINNs for phase field analysis in brittle fracture
• Towards Unified AI-Driven Fracture Mechanics: The Extended Deep Energy Method (XDEM)
• A multiphysics deep energy method for fourth-order phase-field fracture with piezoresistive self-sensing

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