arXiv：cs.LG（机器学习，全量分类）· Yinghao Cheng, Gengxiang Chen, Xu Liu, Qinglu Meng, Yixin Jing, Xiangguo Tang, Wenping Mou, Lihui Wang, Yingguang Li·· 5 小时前AI 评分34
几何-物理混淆损害跨域 PDE 学习
Geometry-physics confounding impairs PDE learning across varying domains
AI 导读
研究指出几何-物理混淆是跨域 PDE 学习的统一失效机制：在前向算子学习中降低数据效率与泛化能力，在方程发现中导致参数偏差、遗漏控制项和虚假项。作者提出去混淆框架，显式建模已知的几何到算子变换，在五个算子学习基准上提升预测与数据效率，并在演化域系统中将留出 PDE 残差降低两个数量级以上。
正文
Abstract:Learning partial differential equation (PDE) dynamics across varying domains is central to predictive modelling and data-driven discovery of governing equations. However, geometric variation alters both field representation and the governing differential operators, confounding geometric effects with intrinsic physical properties in the observed dynamics. This work identifies geometry-physics confounding as a unified failure mechanism for PDE learning across varying domains. In forward operator learning, this confounding increases the burden of inferring geometry-dependent operator changes from finite data, reducing data efficiency and generalisation. In equation discovery, omitting geometry-induced operators misspecifies the candidate library, leading to biased parameters, missed governing terms and spurious terms. We propose a de-confounding framework that makes the known geometry-to-operator transformation explicit. Geometry-induced coefficient fields improve prediction and data efficiency across five operator-learning benchmarks, while geometry-complete candidate libraries recover the generating equations and reduce held-out PDE residuals by more than two orders of magnitude in both evolving-domain systems. By separating known geometric action from intrinsic physics, the proposed framework supports more reliable and data-efficient PDE learning across scientific and engineering problems with varying geometries.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2609.38623 [cs.LG] |
| (or arXiv:2609.38623v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.38623 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Gengxiang Chen [view email]
[v1]
Tue, 29 Sep 2026 22:24:16 UTC (13,656 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org