# CASML 2024 - Scientific Machine Learning Challenge — Data

来源：https://www.kaggle.com/competitions/casml-2024-scientific-machine-learning-challenge/data

采集时间：2026-10-19T20:53:19Z

# Dataset Description

In this competition, participants will develop Physics-Informed Neural Networks (PINNs) to solve the given two-dimensional Convection-Diffusion (CD2D) equation. Unlike traditional machine learning tasks, no training dataset is provided because the goal is to learn the underlying physics of the problem within the specified domain.

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# Provided Data

The only dataset provided is the **test dataset**, which includes the coordinates of test points within the unit square domain \\([0,1] \times [0,1]\\).  

## **File**: `test.csv`  
This file contains the following columns:
- `x`: \(x\)-coordinate of the test point  
- `y`: \(y\)-coordinate of the test point  

Participants must predict the value of \(u(x, y)\), the solution of the CD2D equation, at these coordinates.

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## **Submission Format**

Participants must submit a file named `submission.csv` with the following columns:
1. `x`: \(x\)-coordinate of the test point (as provided in `test.csv`)  
2. `y`: \(y\)-coordinate of the test point (as provided in `test.csv`)  
3. `u`: Predicted solution of the PDE at the given test point  

The submission file must include predictions for **all** test points in the test dataset.

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## **Key Points**  
- **No training data**: The task focuses on developing a PINN that inherently incorporates the physics of the problem.  
- **Test set only**: The provided `test.csv` file specifies the coordinates where predictions are required.  
- **Evaluation**: Predictions will be evaluated based on the L2 error metric compared to the exact solution.  

Good luck, and may the best model win! 🚀