A Python library for solving ice sheet modeling problems using Physics Informed Neural Networks, PINNICLE v1.0

Abstract. Predicting the future contributions of the ice sheets to sea level rise remains a significant challenge due to our limited understanding of key physical processes (e.g., basal friction, ice rheology) and the lack of observations of critical model inputs (e.g., bed topography). Traditional numerical models typically rely on data assimilation methods to estimate these variables by solving inverse problems based on conservation laws of mass, momentum, and energy. However, these methods are not versatile and require extensive code development to incorporate new physics. Moreover, their dependence on data alignment within computational grids hampers their adaptability, especially in the context of sparse data availability in space and time. To address these limitations, we developed PINNICLE (Physics-Informed Neural Networks for Ice and CLimatE), an open-source Python library dedicated to ice sheet modeling. PINNICLE seamlessly integrates observational data and physical laws, facilitating the solution of both forward and inverse problems within a single framework. PINNICLE currently supports a variety of conservation laws, including the Shelfy-Stream Approximation (SSA), Mono-Layer Higher-Order (MOLHO) models, and mass conservation equations, for both time-independent and time-dependent simulations. The library is user-friendly, requiring only the setting of a few hyperparameters for standard modeling tasks, while advanced users can define custom models within the framework. Additionally, PINNICLE is based on the DeepXDE library, which supports widely-used machine learning packages such as TensorFlow, PyTorch, and JAX, enabling users to select the backend that best fits their hardware. We describe here the implementation of PINNICLE and showcase this library with examples across the Greenland and Antarctic ice sheets for a range of forward and inverse problems.