Update README.md

README.md

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----
-license: apache-2.0
----
+---
+license: mit
+task_categories:
+- image-to-3d
+tags:
+- mathematics
+- partial-differential-equations
+- computational fluid dynamics
+- physics
+- neural operator
+size_categories:
+- 1K<n<10K
+---
+# Navier Stokes Dataset of Isotropic Turbulence in a periodic box
+
+<!-- Provide a quick summary of the dataset. -->
+
+The dataset for tensor-to-tensor or trajectory-to-trajectory neural operators, generated from Navier-Stokes equations 
+to model the isotropic turbulence [1] such that the spectra satisfy the inverse cascade discovered by A.N. Kolmogorov [2].
+
+[1]: McWilliams, J. C. (1984). The emergence of isolated coherent vortices in turbulent flow. *Journal of Fluid Mechanics*, 146, 21-43.
+[2]: Kolmogorov, A. N. (1941). The local structure of turbulence in incompressible viscous fluid for very large Reynolds Numbers. *Dokl. Akad. Nauk SSSR*, 30, 301.
+
+## Dataset Details
+
+### Dataset Description
+
+<!-- Provide a longer summary of what this dataset is. -->
+
+The dataset contains several cases of isotropic turbulence modeled by Navier-Stokes equations. The data are generated either 
+by a pseudo-spectral solver with 4th-order Runge-Kutta for the convection term, or a higher order Finite Volume IMEX methods. 
+The different initial conditions have different peak wavenumbers of O(1), and eventually their spectra all converge to the Kolmogorov
+inverse cascade.
+
+- **Curated by:** S. Cao
+- **Funded by National Science Foundation:** NSF award DMS-2309778
+- **License:** MIT license
+
+### Dataset Sources [optional]
+
+<!-- Provide the basic links for the dataset. -->
+
+- **Repository:** [https://github.com/scaomath/torch-cfd](https://github.com/scaomath/torch-cfd)
+- **Paper:** [More Information Needed]
+- **Demo:**
+  - [The classical Kolmogorov inverse cascade with a solenoidal forcing and small drag.](https://github.com/scaomath/torch-cfd/blob/main/examples/Kolmogrov2d_rk4_cn_forced_turbulence.ipynb)
+  - [The fast training using the data with a small number of vortices.](https://github.com/scaomath/torch-cfd/blob/main/examples/ex2_SFNO_train_fnodata.ipynb)
+  - [The fast converging to the inverse cascade.](https://github.com/scaomath/torch-cfd/blob/main/examples/ex2_SFNO_5ep_spectra.ipynb)
+
+## Dataset Structure
+
+<!-- This section provides a description of the dataset fields, and additional information about the dataset structure such as criteria used to create the splits, relationships between data points, etc. -->
+
+Each individual chunk of data is pickled in single-file format.
+
+## Dataset Creation
+
+### TO-DO
+
+## Citation
+
+<!-- If there is a paper or blog post introducing the dataset, the APA and Bibtex information for that should go in this section. -->
+
+```bibtex
+@article{2024SpectralRefiner,
+  title={Spectral-Refiner: Fine-Tuning of Accurate Spatiotemporal Neural Operator for Turbulent Flows},
+  author={Shuhao Cao and Francesco Brarda and Ruipeng Li and Yuanzhe Xi},
+  journal={arXiv preprint arXiv:2405.17211},
+  year={2024},
+  primaryClass={cs.LG}
+}
+```
+
+
+