# Physics-Encoded Inverse Modeling for Arctic Snow Depth Estimation

arXiv: https://arxiv.org/abs/2601.17074 · HTML: https://mlsanity.com/paper/2601.17074/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 25 references that are in the map.
- First posted on arXiv 23 Jan 2026.

## Builds on (most cited first, 17 of 17)

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- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [SwitchNet: a neural network model for forward and inverse scattering problems](https://mlsanity.com/paper/1810.09675/) (2018)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [PhysiX: A Foundation Model for Physics Simulations](https://mlsanity.com/paper/2506.17774/) (2025)
- [Solving Electrical Impedance Tomography with Deep Learning](https://mlsanity.com/paper/1906.03944/) (2019)
- [Robust Inverse Framework using Knowledge-guided Self-Supervised Learning: An application to Hydrology](https://mlsanity.com/paper/2109.06429/) (2021)
- [Knowledge-guided Machine Learning: Current Trends and Future Prospects](https://mlsanity.com/paper/2403.15989/) (2024)
- [Deep-Learning based Inverse Modeling Approaches: A Subsurface Flow Example](https://mlsanity.com/paper/2007.15580/) (2020)
- [Hard Encoding of Physics for Learning Spatiotemporal Dynamics](https://mlsanity.com/paper/2105.00557/) (2021)

## Abstract (arXiv)

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.