arXiv:2603.25779cs.LGcs.AI2026-03

用深度学习预测任意地点地下水位,融合物理规律提升精度与可信度。

Pure and Physics-Guided Deep Learning Solutions for Spatio-Temporal Groundwater Level Prediction at Arbitrary Locations

  • 基于注意力机制构建纯数据驱动模型STAINet,处理稀疏水位与密集气象数据。
  • 引入物理约束后模型在滚动测试中平均误差仅0.16%,相关系数达0.58。
  • 通过物理方程监督增强可解释性,适合水资源管理与气候建模研究者。

地下水是水循环的关键组成部分,但其时空变化关系复杂且依赖具体环境,建模极具挑战。传统机理模型虽科学性强,却受限于计算成本、简化假设和校准需求。近年来,数据驱动方法尤其是深度学习展现出强大潜力。本文提出一种基于注意力机制的纯深度学习模型STAINet,用于预测任意位置、不定数量点的周尺度地下水位,融合稀疏水位观测与密集气象信息。为进一步提升模型可信度与泛化能力,引入多种物理引导策略:在STAINet-IB中加入归纳偏置以估计控制方程分量;在STAINet-ILB中采用学习偏置,通过额外损失项监督方程分量估计;在STAINet-ILRB中引入领域专家提供的补给区信息。其中STAINet-ILB表现最优,在滚动预测设置下中位数MAPE为0.16%,KGE达0.58,且能合理预测方程分量,揭示其物理合理性。物理引导方法显著提升模型泛化性与可信度,为下一代混合型深度学习地球系统模型奠定基础。

原文摘要 · Abstract (English)

Groundwater represents a key element of the water cycle, yet it exhibits intricate and context-dependent relationships that make its modeling a challenging task. Theory-based models have been the cornerstone of scientific understanding. However, their computational demands, simplifying assumptions, and calibration requirements limit their use. In recent years, data-driven models have emerged as powerful alternatives. In particular, deep learning has proven to be a leading approach for its design flexibility and ability to learn complex relationships. We proposed an attention-based pure deep learning model, named STAINet, to predict weekly groundwater levels at an arbitrary and variable number of locations, leveraging both spatially sparse groundwater measurements and spatially dense weather information. Then, to enhance the model's trustworthiness and generalization ability, we considered different physics-guided strategies to inject the groundwater flow equation into the model. Firstly, in the STAINet-IB, by introducing an inductive bias, we also estimated the governing equation components. Then, by adopting a learning bias strategy, we proposed the STAINet-ILB, trained with additional loss terms adding supervision on the estimated equation components. Lastly, we developed the STAINet-ILRB, leveraging the groundwater body recharge zone information estimated by domain experts. The STAINet-ILB performed the best, achieving overwhelming test performances in a rollout setting (median MAPE 0.16%, KGE 0.58). Furthermore, it predicted sensible equation components, providing insights into the model's physical soundness. Physics-guided approaches represent a promising opportunity to enhance both the generalization ability and the trustworthiness, thereby paving the way to a new generation of disruptive hybrid deep learning Earth system models.

地下水预测深度学习物理引导时空建模

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。