# A Physics-Constrained Neural Differential Equation Framework for Data-Driven Snowpack Simulation

arXiv: https://arxiv.org/abs/2412.06819 · HTML: https://mlsanity.com/paper/2412.06819/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 81 references that are in the map.
- First posted on arXiv 3 Dec 2024.

## Builds on (most cited first, 3 of 3)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networks](https://mlsanity.com/paper/2007.07442/) (2020)
- [Fashionable Modelling with Flux](https://mlsanity.com/paper/1811.01457/) (2018)

## Abstract (arXiv)

This paper presents a physics-constrained neural differential equation framework for parameterization, and employs it to model the time evolution of seasonal snow depth given hydrometeorological forcings. When trained on data from multiple SNOTEL sites, the parameterization predicts daily snow depth with under 9% median error and Nash Sutcliffe Efficiencies over 0.94 across a wide variety of snow climates. The parameterization also generalizes to new sites not seen during training, which is not often true for calibrated snow models. Requiring the parameterization to predict snow water equivalent in addition to snow depth only increases error to ~12%. The structure of the approach guarantees the satisfaction of physical constraints, enables these constraints during model training, and allows modeling at different temporal resolutions without additional retraining of the parameterization. These benefits hold potential in climate modeling, and could extend to other dynamical systems with physical constraints.