arXiv：cs.LG· Hyeonsu Lee, Jihoon Jeong·· 4 小时前AI 评分34
基于条件流匹配的域信息自适应采样，提升金属增材制造 PINN 泛化能力
Domain-informed Adaptive Sampling for Generalizable PINNs in Metal Additive Manufacturing via Conditional Flow Matching
AI 导读
研究者提出一种面向金属增材制造的两阶段自适应采样框架，用条件 Flow Matching 模型学习不同工艺条件下的高残差分布，再与域信息基分布混合生成搭配点以精修 PINN 预测器。在相同搭配点预算下，该方法相对 L₂ 误差平均降低 62.1%，持续优于现有 PINN 基线。作者称这是金属增材制造中首个面向 PINN 的自适应采样策略。
正文
Abstract: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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.09126 [cs.LG] |
| (or arXiv:2610.09126v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.09126 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Hyeonsu Lee [view email]
[v1]
Tue, 6 Oct 2026 21:19:32 UTC (11,361 KB)
来源：arXiv：cs.LG · arxiv.org