Universal Functional Regression with Neural Operator Flows

The repository contains codes for Universal Functional Regression with Neural Operator Flows

(Appeared at Transaction on Machine Learning Research (TMLR), 2024 by Shi, Yaozhong and Gao, Angela F and Ross, Zachary E and Azizzadenesheli, Kamyar)

Requirements

PyTorch 1.12.1 scikit-learn 1.2.2

Files

Files	Descriptions
Generation tasks
1D_domain_decomposed_GP.ipynb	resolution=256, generation task for 1D GP data
1D_domain_decomposed_TGP.ipynb	resolution=256, generation task for 1D Truncated GP data
2D_domain_decomposed_GRF.ipynb	resolution=64x64, generation task for 2D GRF data
2D_domain_decomposed_TGRF.ipynb	resolution=64x64, generation task for 2D Truncated GRF data
1D_codomain_GP.ipynb	resolution=256, sliding regularization used, generation task for 1D GP data, codomain OpFlow
2D_codomain_TGRF.ipynb	resolution=64x64, generatin tasks for 2D Truncated GRF data, codomain OpFlow
Regression tasks
1D_domain_decomposed_GP_prior.ipynb	resolution=128
1D_domain_decomposed_GP_regression.ipynb	duplicate the results of classical GPR
1D_domain_decomposed_TGP_prior.ipynb	resolution=128
1D_domain_decomposed_TGP_regression.ipynb	Non-Gaussian process regression
2D_domain_decomposed_GRF_prior.ipynb	resolution=32x32
2D_domain_decomposed_GRF_regression_case1.ipynb	regression with scatter observations
2D_domain_decomposed_GRF_regression_case2.ipynb	regression with strip observations
1D_codomain_GP_prior.ipynb	resolution=128
1D_codomain_GP_regression.ipynb	codomain GP Regression
SGLD sampling
samplers.py
SGLD.py
Comments	sliding regularization trick used in some files can be useful for others challenging tasks, feel free to add that on for all tasks

Datasets

Synthetic dataset can be directly generated in the training files, earthquake datasets used in the paper can be downloaded from kik-net website kik-net

Reference:

@article{shi2024universal, title={Universal Functional Regression with Neural Operator Flows}, author={Shi, Yaozhong and Gao, Angela F and Ross, Zachary E and Azizzadenesheli, Kamyar}, journal={arXiv preprint arXiv:2404.02986}, year={2024} }