面向金属增材制造中可泛化PINN的基于条件流匹配的域感知自适应采样
Domain-informed Adaptive Sampling for Generalizable PINNs in Metal Additive Manufacturing via Conditional Flow Matching
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- Texas A&M University（德克萨斯A&M大学）
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中文总结 AI 辅助
针对金属增材制造中PINN热建模依赖手工静态采样、泛化差的问题，提出基于条件流匹配的两阶段自适应采样策略，在相同配点预算下平均相对L2误差降低62.1%。
中文摘要 AI 辅助
精确的热建模对于金属增材制造（AM）中理解工艺-结构-性能链至关重要。物理信息神经网络（PINNs）通过在配点上最小化基于物理的残差损失，提供了有效的替代热建模方法。然而，先前的工作通常依赖于手工设计的静态配点采样策略，这些策略既缺乏原则性，也无法在不同工艺条件下扩展，阻碍了其泛化能力。在本工作中，我们通过经验风险最小化提供理论分析，表明对于泛化而言，考虑工艺条件的自适应采样严格优于传统静态采样。基于这一见解，我们提出了一种两阶段框架内的自适应采样策略：（1）一个条件流匹配模型，学习不同工艺条件下近似的高残差分布；（2）一种混合采样策略，将该分布与域信息基础分布相结合，以生成用于优化PINN预测器的自适应配点。在金属增材制造数值基准上的实验表明，我们的方法在相同配点预算下，通过捕捉文献中常被忽视的依赖工艺的散热区域，平均相对$L_2$误差降低了62.1%，持续优于最先进的PINN基线。据作者所知，这是金属增材制造中PINN的首个自适应采样策略，有助于增强泛化能力和更广泛的适用性。
英文摘要
Accurate thermal modeling is essential in metal additive manufacturing (AM) for understanding the process-structure-property chain. Physics-informed neural networks (PINNs) offer effective surrogate thermal modeling by minimizing physics-based residual losses at collocation points. However, prior works typically rely on manually-crafted, static collocation sampling strategies, which are neither principled nor scalable across process conditions, hindering their generalization capability. In this work, we provide theoretical analysis through empirical risk minimization, showing that process condition-aware adaptive sampling is strictly more favorable than conventional static sampling for generalization. Building on this insight, we propose an adaptive sampling strategy within a two-stage framework: (1) a conditional Flow Matching model that learns approximate high-residual distributions across different process conditions, and (2) a mixed sampling strategy combining this distribution with a domain-informed base distribution to generate adaptive collocation points for refining the PINN predictor. Experiments on metal AM numerical benchmarks demonstrate that our method consistently outperforms state-of-the-art PINN baselines, achieving an average 62.1\% reduction in relative $L_2$ error under an identical collocation budget, by capturing process-dependent heat dissipation regions often overlooked in the literature. To the authors' knowledge, this is the first adaptive sampling strategy for PINNs in metal AM, contributing to the enhanced generalization and broader applicability.
