用物理约束的深度学习模型，估算极地海冰上稀疏观测下的积雪深度。
Physics-Encoded Inverse Modeling for Arctic Snow Depth Estimation
- 结合LSTM与对比学习，用物理规律编码参数以增强时间依赖建模。
- 相比基线模型平均降低24.4%均方误差，参数估计下提升17.3%。
- 适合数据稀疏的气候反演任务，尤其适用于缺乏直接观测的极地研究。
在观测稀疏且目标变量仅间接相关的时间演化反问题中，准确估计未观测量仍具挑战性。在北极气候应用中，海冰上的积雪深度无法直接从常用再分析产品中获取，需通过相关物理与环境变量推断。为此，我们提出物理编码反演框架（PhysE-Inv），融合序列深度学习与物理编码参数估计模块，在稀疏观测条件下实现反演估计。该框架采用LSTM编码器-解码器捕捉时间依赖性，并引入对比学习提升特征表示一致性。通过学习结构化的物理编码参数并融合观测输入，估算积雪深度代理变量。在所提出的代理评估框架下，PhysE-Inv优于所有基线模型，相较基线平均降低24.4%均方误差，参数估计设置下较最强基线提升17.3%。结果表明，物理编码建模方法在缺乏直接观测的数据稀缺领域具有潜力。
原文摘要 · Abstract (English)
Accurate estimation of unobserved quantities in time-varying inverse problems remains challenging when observations are sparse and only indirectly related to the target variable. In Arctic climate applications, snow depth over sea ice is not directly available in commonly used reanalysis products and must instead be inferred from related physical and environmental variables. To address this challenge, we introduce Physics-Encoded Inverse Modeling (PhysE-Inv), a framework that combines sequential deep learning with a physics-encoded parameter estimation module for inverse estimation under sparse observational conditions. PhysE-Inv uses an LSTM encoder-decoder to capture temporal dependencies and incorporates contrastive learning to improve the consistency of learned representations. The framework learns structured physics-encoded parameters that are integrated with observational inputs to estimate snow depth proxies. Under the proposed proxy evaluation framework, PhysE-Inv outperforms all evaluated baselines, achieving an average MSE reduction of 24.4\% compared with baseline models and a 17.3\% improvement over the strongest baseline under the parameter estimation setting. These results demonstrate the potential of physics-encoded modeling approaches for estimating unobserved quantities in data-scarce domains where direct observations are limited.
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