This dataset can serve as a benchmark for models used to solve PDEs.

Given low-resolution data, models are required to predict high-resolution solutions and perform extrapolation.

Update

There is a private competition (in Chinese) based on this dataset. Feel free to participate in this competition.

The baseline (in Chinese) is in this repo

Description of the Rayleigh–Bénard Convection

The Rayleigh–Bénard Convection of this dataset is as follows:

$$ \frac{\partial{u_x}}{\partial{t}} +u_x\frac{\partial{u_x}}{\partial{x}}+u_y\frac{\partial{u_x}}{\partial{y}}=-\frac{1}{\rho}\frac{\partial{P}}{\partial{x}}+ R(\frac{\partial^2{u_x}}{\partial{x^2}}+\frac{\partial^2{u_x}}{\partial{y^2}}) $$ $$ \frac{\partial{u_y}}{\partial{t}} +u_x\frac{\partial{u_y}}{\partial{x}}+u_y\frac{\partial{u_y}}{\partial{y}}=-\frac{1}{\rho}\frac{\partial{P}}{\partial{y}}+ R(\frac{\partial^2{u_y}}{\partial{x^2}}+\frac{\partial^2{u_y}}{\partial{y^2}})+T $$ $$ \frac{\partial{T}}{\partial{t}}+u_x\frac{\partial{T}}{\partial{x}}+u_y\frac{\partial{T}}{\partial{y}}=P(\frac{\partial^2{T}}{\partial{x^2}}+\frac{\partial^2{T}}{\partial{y^2}}) $$ $$ \frac{\partial{u_x}}{\partial{x}}+\frac{\partial{u_y}}{\partial{y}}=0 $$ $$ R=\sqrt{\frac{Pr}{Ra}} $$ $$ P=\sqrt{\frac{1}{RaPr}} $$

where u_x and u_y are the x component and y component of the velocity, respectively. T and P are dimensionless temperature and pressure, respectively. Ra=1e6 is the Rayleigh number, Pr=1 is the Prandtl number, and ρ=1 is the dimensionless density.

Description of files

This dataset contains three files.

• t50_ra1e6_pr1_s42_train_lr.npz: the low-resolution data of 0-44.75s.
• test.csv: the test dataset.
• gt.csv: the ground truth of the test dataset.

Columns

• id: The ID of each sample
• t: the time component of the coordinate
• x: the x component of the coordinate
• y: the y component of the coordinate
• u: the x component of the velocity
• w: the y component of the velocity
• T: the dimensionless temperature
• P: the dimensionless pressure