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} }