The accurate estimation of Arctic snow depth remains a critical time-varying inverse problem due to the scarcity 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, namely an LSTM Encoder-Decoder with Multi-head Attention and contrastive learning, with physics-guided inference. Our core innovation lies in a 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 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. Beyond Arctic snow depth, PhysE-Inv can be applied broadly to other noisy, data-scarce problems in Earth and climate science.

翻译：北极雪深的精确估计，由于相关海冰参数的稀缺性，仍然是一个关键的时变反问题。现有的基于过程的模型和数据驱动模型要么对稀疏数据高度敏感，要么缺乏气候关键应用所需的物理可解释性。为弥补这一不足，我们提出了PhysE-Inv，这是一个新颖的框架，它将一个复杂的序列架构——即带有多头注意力和对比学习的LSTM编码器-解码器——与物理引导的推理相结合。我们的核心创新在于一种物理约束的反演方法。该方法首先利用流体静力平衡前向模型作为目标公式代理，从而在缺乏直接地面真值的情况下实现有效学习；其次，它在潜在空间上使用重建物理正则化，以从噪声、不完整的时序输入中动态发现隐藏的物理参数。与最先进的基线方法相比，PhysE-Inv显著提高了预测性能，误差降低了20%，同时与经验方法相比，展现出更优的物理一致性和对数据稀疏性的鲁棒性。除了北极雪深，PhysE-Inv还可广泛应用于地球与气候科学中其他存在噪声、数据稀缺的问题。