A DIFFerentiable neural-network solver for data assimilation of ICE shelves written in JAX.
DIFFICE_jax is a Python package that solves the depth-integrated Stokes equation for ice shelves, and can be adopted for ice sheets by modifying the partial differential equations (PDE) in the neural network loss function. It uses PDEs to interpolate descretized remote-sensing data into meshless and differentible functions, and infer ice shelves' viscosity structure via back-propagation and automatic differentiation (AD). The algorithm is based on physics-informed neural networks (PINNs) and implemented in JAX. The DIFFICE_jax package involves several advanced features in addition to vanilla PINNs algorithms, including collocation points resampling, non-dimensionalization of the data adnd equations, extended-PINNs (XPINNs) (see figure below), viscosity exponential scaling function, which are essential for accurate inversion. The package is designed to be user-friendly and accessible for beginners. The Github respository also provides tutorial and real-data examples for users at different levels to have a good command of the package.
The build of the code is tesed on Python version (3.9, 3.10 and 3.11) and JAX version (0.4.20, 0.4.23, 0.4.26)
You can install the package using pip as follows:
python -m pip install DIFFICE_jaxThe documentation for the algorithms and the mathematical formulation for the data assimilation of ice shelves
are provided in the docs folder. Documentations for the synthetic examples and real-data examples are given in the tutorial folder and examples
folders, respectively.
We highly recommend new users to get familar with the software by reading the document and playing with the synthetic example prepared in the tutorial folder. The synthetic example allow users to generate the synthetic data of velocity and thickness of an ice-shelf flow in a rectangular domain with any given viscosity profile. Users can then use the PINNs code prepared in the folder to infer the given viscosity from the synthetic code. We provide a Colab Notebook
that allows users to compare the given viscosity with the PINN inferred viscosity to validate the accuracy of PINNs on inverse problem.
The inversion codes with the real velocity and thickness data for four different ice shelves surrounding the Antarctica are provided in the examples folders. The original source and the required format for the datasets are described here. In the paper, we
summarized six algorithm features of the DIFFICE_jax package beyond the vanilla PINNs code. We provide four example codes in examples that can be used to analyze different ice-shelf datasets. For each example code, the corresponding implemented features and the ice-shelf dataset it can analyze are listed in the table below.
| Example codes | Feature # | Ice shelf |
|---|---|---|
| train_pinns_iso | (1), (2), (3), (4) | Amery, Larsen C, synthetic |
| train_pinns_aniso | (1), (2), (3), (4), (6) | Amery, Larsen C |
| train_xpinns_iso | (1), (2), (3), (4), (5) | Ross, Ronne-Filchner |
| train_xpinns_aniso | (1), (2), (3), (4), (5), (6) | Ross, Ronne-Filchner |
Apart from the Python scripts to run locally, we also provide Colab Notebooks for both the synthetic and real
ice-shelf examples. They are provided in the tutorial and examples folders for a synthetic ice shelf and real ice shelves,
respectively.
This package is written by Yongji Wang and maintained by Yongji Wang (yongjiw@stanford.edu) and Ching-Yao Lai (cyaolai@stanford.edu). If you have questions about this code and documentation, or are interested in contributing the development of the DIFFICE_jax package, feel free to get in touch.
DIFFICE_jax is an open-source software. All code within the project is licensed under the MIT License. For more details, please refer to the LICENSE file.
BibTex:
@article{wang2022discovering,
title={Discovering the rheology of Antarctic Ice Shelves via physics-informed deep learning},
author={Wang, Yongji and Lai, Ching-Yao and Cowen-Breen, Charlie},
year={2022},
doi = {https://doi.org/10.21203/rs.3.rs-2135795/v1},
}