arXiv：cs.AI· Akshay Dhalpe, Arnab Chattopadhyay, Shahriar Bakrani Balani, Eric Cortan\'ea, Sasu Tarkoma·· 18 小时前
pi-Net：数据稀缺系统下可微物理头的经验潜表征
pi-Net: Empirical Latent Representations for Differentiable Physics Heads in Data-Scarce Systems
AI 导读
pi-Net 是一种物理信息潜变量模型，通过编码器将输入映射到物理归一化潜空间、再由可微物理头解码输出，用于解决将量纲分析引入有向计算图后产生的欠定系统问题。在数据稀缺的 GMAW 真实案例中，仅用 60 个实验样本即达到 R2 0.864，显著优于纯数据驱动基线，并提供因果的工艺级可解释性。
正文
Abstract:Developing reliable predictive models for multi-physics systems often forces a compromise between computationally demanding physical simulators and data-hungry, opaque machine learning (ML) algorithms. While incorporating dimensional analysis into directed computation graphs offers a structurally sound alternative to explicitly solving partial differential equations (PDEs), such formulations typically yield underdetermined systems that act as imperfect simulators. We introduce pi-Net, a physics-informed latent variable model that resolves these imperfect simulators. The hybrid pi-Net architecture consists of an encoder that maps inputs into physically normalized latent space, which are then decoded into final predictions by a differentiable physics head. Evaluated on a real-world, data-scarce Gas Metal Arc Welding (GMAW) case study, the framework achieves an R2 of 0.864 with only 60 experimental samples. The results demonstrate that pi-Net significantly outperforms purely data-driven baselines in data-scarce regimes while providing causal, process-level explainability.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.16504 [cs.LG] |
| (or arXiv:2610.16504v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.16504 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Arnab Chattopadhyay [view email]
[v1]
Mon, 12 Oct 2026 09:52:34 UTC (211 KB)
来源：arXiv：cs.AI · arxiv.org