Dataset for MRes Thesis: Probabilistic Operator Learning for Climate Model Parameterisation

This dataset was collated for use in experiments presented in the MRes Thesis "Probabilistic Operator Learning for Climate Model Parameterisation" submitted to the University of Cambridge.All data included was generated by other researchers, this is simply a subset to allow easy reproduction of the experiments contained in the work above.

The data for the Burgers' equation (burgers_data_R10.mat) and the Darcy Flow (piececonst_r421_N1024_smooth1.mat, piececonst_r421_N1024_smooth2.mat) experiments were generated by Lu et al. (2022). Creative Commons Attribution Non Commercial Share Alike 4.0 International applies.

The data for the Helmholtz (Helmholtz_inputs.npy, Helmholtz_outputs.npy) and Navier-Stokes (NavierStokes_inputs.npy, NavierStokes_outputs.npy) experiments were generated by de Hoop et al. (2022). Creative Commons Attribution 4.0 International applies.

References:

1. Lu L, Meng X, Cai S, Mao Z, Goswami S, Zhang Z, et al. A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data. Computer Methods in Applied Mechanics and Engineering. 2022 Apr 1;393:114778.

2. de Hoop MV, Huang DZ, Null EQ, Stuart AM. The Cost-Accuracy Trade-Off in Operator Learning with Neural Networks. JML. 2022 Jun;1(3):299–341.

本数据集为适配提交至剑桥大学的研究型硕士学位论文《概率算子学习在气候模型参数化中的应用（Probabilistic Operator Learning for Climate Model Parameterisation）》中的相关实验而整理汇编。本数据集收录的全部数据均由其他研究者生成，仅为便于复现上述论文中的实验而截取的子集。

伯格斯方程（Burgers' equation）实验所用数据（文件名为burgers_data_R10.mat）与达西流（Darcy Flow）实验所用数据（文件名为piececonst_r421_N1024_smooth1.mat、piececonst_r421_N1024_smooth2.mat）均由Lu等人（2022）生成，适用知识共享署名-非商业性使用-相同方式共享4.0国际许可协议。

亥姆霍兹（Helmholtz）实验所用数据（文件名为Helmholtz_inputs.npy、Helmholtz_outputs.npy）与纳维-斯托克斯（Navier-Stokes）实验所用数据（文件名为NavierStokes_inputs.npy、NavierStokes_outputs.npy）均由de Hoop等人（2022）生成，适用知识共享署名4.0国际许可协议。

参考文献：
1. Lu L, Meng X, Cai S, Mao Z, Goswami S, Zhang Z 等. 基于FAIR数据的两类神经算子（含实用扩展）的全面公平比较. 应用力学与工程计算机方法. 2022年4月1日;393:114778.
2. de Hoop MV, Huang DZ, Null EQ, Stuart AM. 神经网络算子学习中的成本-精度权衡. 机器学习期刊（JML）. 2022年6月;1(3):299–341.