arXiv：cs.LG· Johanna Moser, Christopher Albert, Sascha Ranftl·· 4 小时前
幽灵任务（Ghost tasking）：让参量化高斯过程求解线性微分方程
Ghost tasking for parametrized Gaussian Processes solving linear differential equations
AI 导读
研究者提出"幽灵任务"（ghost tasking）方法，通过引入辅助任务，使任何不可参量化系统变得等效可参量化，从而在保持输出任务数和潜函数数量较低的情况下，算法化构建参量化高斯过程。该方法在逆问题场景中表现尤佳，即使在数据极少时依然有效，并已在三个实验中与目前唯一适用于全部实验的对照方法进行了系统比较。论文同时给出了两个计算机代数程序所需的语法与说明，用于计算多项式或有理系数系统的参量化。
正文
Abstract:Physics-informed machine learning has gained significant attention in recent years. In regimes of limited data, parametrized Gaussian processes have become popular. Existing approaches, however, often face limitations, such as requiring parametrizable (also called controllable) systems or a large number of output tasks. In this work, we introduce a systematic procedure we call "ghost tasking", using auxiliary tasks to circumvent these limitations. We prove that such ghost tasks can render any non-parametrizable system effectively parametrizable, enabling algorithmic construction of parametrized Gaussian Processes while keeping the number of required tasks (i.e. output dimensions) and latent functions low. We find that ghost tasking performs especially well in an inverse problem setting, even with very few available data. We show the usage and power of ghost tasking in three experiments, providing systematic comparisons to the only other currently available method applicable to all experiments. We provide necessary syntax and explications for two computer algebra programs that compute parametrizations for systems with polynomial or rational coefficients. Our theoretical results extend to systems with meromorphic functions.
| Comments: | 46 pages, 14 figures, for reproducibility: this https URL |
| Subjects: | Computational Physics (physics.comp-ph); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.12009 [physics.comp-ph] |
| (or arXiv:2610.12009v1 [physics.comp-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12009 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Johanna Moser [view email]
[v1]
Thu, 8 Oct 2026 14:10:51 UTC (2,880 KB)
来源：arXiv：cs.LG · arxiv.org