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

TL;DR

Arctic snow depth estimation is hindered by sparse, noisy observations and non-unique inversions. The authors propose PhysE-Inv, a physics-encoded inverse modeling framework that uses a hydrostatic-balance proxy as a target-formulation and enforces physical consistency through a surjective inverse and physics-guided contrastive learning. The approach combines an LSTM encoder-decoder with multi-head attention to derive a latent representation $z_n$, from which dynamic parameters $(\alpha_n,\beta_n,\gamma_n)$ are inferred and used in a reconstruction proxy for $h_s$, guided by a physics loss $ ext{L}_{PE-pred}$ and a PGCL objective. Compared with several baselines, PhysE-Inv yields improved predictive accuracy and robustness to data sparsity, demonstrating better physical consistency and resilient inverse learning for Arctic snow-depth estimation.

Abstract

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.

Figures (6)

• Figure 1: The Physics-Encoded Inverse ($\text{PhysE-Inv}$) framework outlines the fusion of physical constraints, representation learning, and a surjective inverse mapping approach based on the hydrostatic balance proxy. $T$ represents the final observation time in the input sequence.
• Figure 2: Comparison of model performance: box plot of snow depth deviations.
• Figure 3: Time series of predicted and estimated mean snow depth seasonal pattern
• Figure 4: Map showing the spatial extent of the central Arctic Ocean, highlighting (orange line) the region used for data collection.
• Figure 5: (a) Bijective mapping: unique input-output relationship. (b) Surjective mapping: multiple inputs to one output.