基于相场断裂的条件去噪扩散模型的不确定性感知裂纹扩展预测
Uncertainty-Aware Crack Growth Forecasting via Conditional Denoising Diffusion Models for Phase-Field Fracture
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中文总结 AI 辅助
研究针对传统方法预测脆性裂纹扩展的计算瓶颈，提出基于物理的条件去噪扩散概率模型，可进行全场时空断裂演化预测，能在不修改模型下量化不确定性，有精度提升、跨状态泛化等优势，且推理速度有改进。
中文摘要 AI 辅助
利用传统高保真相场有限元方法准确预测脆性裂纹萌生、扩展和复杂拓扑演化在计算上仍令人望而却步。为克服这些计算瓶颈，提出一种基于物理的条件去噪扩散概率模型（DDPM），用于跨不同加载状态和能量分解方法的全场时空断裂演化预测。生成架构以滚动历史损伤状态为条件，并明确推导运动学代理——相场速度和梯度大小，确保时间连贯性且无物理伪影。主要贡献是在不修改训练模型的情况下进行空间局部不确定性量化。集合方差集中在裂纹分支点（Y形分支处\(\sigma_{max}=0.222\)；四个确定性扩展案例中无高不确定性像素），高\(\sigma\)尾部以90%的精度识别高误差预测——比随机选择提高了18倍。一步裂纹尖端定位在两个验证子集（剪切星型和拉伸光谱）上均实现亚像素精度（平均误差0.12像素），证实跨状态泛化能力。在50步的闭环自回归展开中，DDPM保持Dice = 0.929±0.010，而确定性U-Net在误差累积下降至Dice = 0.423，差距达2.2倍，这确立了随机重采样对长时稳定性的价值。在H100 GPU上每步推理约需3.6秒，比有限元参考快约28倍，比确定性U-Net慢约1000倍，此代价换来了能进行不确定性量化的随机多样性。
英文摘要
The accurate prediction of brittle crack initiation, propagation, and complex topological evolution remains computationally prohibitive when utilizing traditional high-fidelity phase-field finite element methods. To overcome these computational bottlenecks, a physics-informed conditional Denoising Diffusion Probabilistic Model (DDPM) is proposed for the full-field spatiotemporal forecasting of fracture evolution across diverse loading regimes and energy decomposition methods. The generative architecture is conditioned on rolling historical damage states and explicitly derived kinematic proxies -- phase-field velocity and gradient magnitude -- ensuring temporal coherence without non-physical artifacts. The principal contribution is spatially-localized uncertainty quantification without modification to the trained model. Ensemble variance concentrates at crack branching junctions ($σ_\mathrm{max} = 0.222$ at Y-junction bifurcations; zero high-uncertainty pixels in four deterministic propagation cases), while the high-$σ$ tail identifies high-error predictions with 90\% precision -- an 18-fold improvement over random selection. One-step crack tip localization achieves sub-pixel accuracy (0.12 px mean error) across both held-out validation subsets (shear-star and tension-spect), confirming cross-regime generalization. In closed-loop autoregressive rollout over 50 steps, the DDPM maintains Dice = 0.929 $\pm$ 0.010 while a deterministic U-Net collapses to Dice = 0.423 under error accumulation, a 2.2$\times$ gap that establishes the value of stochastic re-sampling for long-horizon stability. Per-step inference requires approximately 3.6 s on an H100 GPU, approximately 28$\times$ faster than the FEM reference and 1{,}000$\times$ slower than a deterministic U-Net a cost that buys the stochastic diversity enabling uncertainty quantification.
