Abstract
The accurate estimation of Arctic snow depth remains a critical time-varying inverse problem due to the extreme scarcity and noise inherent in associated sea ice parameters. Existing process-based and data-driven models are either highly sensitive to sparse data or lack the physical interpretability required for climate-critical applications. To address this gap, we introduce PhysE-Inv, a novel framework that integrates a sophisticated sequential architecture, an LSTM Encoder-Decoder with Multi-head Attention and physics-guided contrastive learning, with physics-guided this http URL core innovation lies in a surjective, physics-constrained inversion methodology. This methodology first leverages the hydrostatic balance forward model as a target-formulation proxy, enabling effective learning in the absence of direct $h_s$ ground truth; second, it uses reconstruction physics regularization over a latent space to dynamically discover hidden physical parameters from noisy, incomplete time-series input. Evaluated against state-of-the-art baselines, PhysE-Inv significantly improves prediction performance, reducing error by 20\% while demonstrating superior physical consistency and resilience to data sparsity compared to empirical methods. This approach pioneers a path for noise-tolerant, interpretable inverse modeling, with wide applicability in geospatial and cryospheric domains.
Abstract (translated)
北极雪深的精确估算仍然是一个关键的时间变化逆问题，由于与之相关的海冰参数极其稀少且存在噪声。现有的基于过程和数据驱动的模型要么对稀疏数据非常敏感，要么缺乏气候应用所需的物理可解释性。为了填补这一空白，我们引入了PhysE-Inv，这是一个新颖的框架，该框架集成了一个复杂的序列架构——LSTM编码器解码器与多头注意机制以及基于物理学引导的对比学习，并在此基础上进行了创新，核心在于一种单射、受物理约束的反演方法。此方法首先利用水静力平衡正向模型作为目标形式化代理，在没有直接 $h_s$ 地面真实值的情况下实现有效学习；其次，它在潜在空间中使用重建物理学正则化来动态发现隐藏的物理参数，从嘈杂、不完整的时序输入中进行挖掘。与最先进的基准相比，PhysE-Inv显著提高了预测性能，误差降低了20%，同时展示了优于经验方法的优异物理一致性和数据稀疏性的鲁棒性。这种方法为耐噪声、可解释逆向建模开创了一条新路径，在地理空间和冰冻圈领域具有广泛的应用前景。
URL
https://arxiv.org/abs/2601.17074
