PhysE-Inv: A Physics-Encoded Inverse Modeling approach for Arctic Snow Depth Prediction

The accurate estimation of Arctic snow depth ($h_s$) 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 inference.Our 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.