Title: PhysERL-Inv: A Physics-Encoded Inverse Modeling Approach for Arctic Snow Depth Prediction
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Inverse modeling, Supervised representation learning, Surjective mapping, Arctic snow depth, Knowledge guidance

Abstract: The integration of domain knowledge with inverse modeling has emerged as a powerful approach for solving complex physical systems in machine learning. While prior research has explored bijective mapping and complex contrastive learning, the potential of surjective mapping in combination with supervised representation learning remains largely unexplored. To address this gap, we propose Physics-encoded Representation Learning for Inverse modeling (PhysERL-Inv), which encodes the hydrostatic balance equation and uses supervised contrastive learning to predict the time evolution of Arctic snow depth. Evaluated against multiple baseline models, PhysERL-Inv significantly improves prediction performance, reducing error by 20% and demonstrating superior physical consistency. Our approach demonstrates the potential of leveraging surjective mapping to solve complex, ill-posed problems, with wide applicability in data-sparse domains.