---
license: cc
language:
- en
tags:
- datasets
- machine-learning
- deep-learning
- physics-modeling
- scientific-ML
- material-point-method
- smooth-particle-hydrodynamics
- MPM
- SPH
- Lagrangian-Dynamics
pretty_name: MPMVerse
size_categories:
- 100K<n<1M
---

# Dataset Card for MPMVerse Physics Simulation Dataset

## Dataset Summary

This dataset contains Material-Point-Method (MPM) simulations for various materials, including water, sand, plasticine, elasticity, jelly, rigid collisions, and melting. Each material is represented as point-clouds that evolve over time. The dataset is designed for learning and predicting MPM-based physical simulations.

## Supported Tasks and Leaderboards

The dataset supports tasks such as:
- **Physics-informed learning**
- **Point-cloud sequence prediction**
- **Fluid and granular material modeling**
- **Neural simulation acceleration**

## Dataset Structure

### Materials and Metadata

The dataset consists of the following materials, each with its own characteristics:

| Material | Num Trajectories | Duration | Full-order Size | Sample Size | Train Size |
|----------|----------------|----------|----------------|-------------|------------|
| Elasticity3D | 8 | 120 | 78,391 | 2K | 20,520 |
| Plasticine3D | 15 | 320 | 5,035 | 1K | 37,680 |
| Sand3D_Long | 5 | 300 | 32,793 | 1K | 14,112 |
| Water3D_Long | 5 | 1000 | 55,546 | 1.5K | 47,712 |
| Sand3D | 15 | 320 | 7,146 | 1.5K | 37,680 |
| Water3D | 15 | 320 | 2,979 | 0.7K | 37,680 |
| Jelly3D | 15 | 200 | 1,659 | 0.5K | 46,560 |
| Collisions3D | 15 | 500 | 8,019 | 3K | 29,640 |
| MultiMaterial2D | - | 1000 | 1.5K | - | 50,745 |
| WaterDrop2D | - | 1000 | 1K | - | 99,500 |
| Sand2D | - | 320 | 2K | - | 94,500 |

### Data Instances

Each dataset file is a dictionary with the following keys:

#### `train.obj/test.pt`
- **particle_type** (list): Indicator for material (only relevant for multimaterial simulations). Each element has shape `[N]` corresponding to the number of particles in the point-cloud.
- **position** (list): Snippet of past states, each element has shape `[N, W, D]` where:
  - `N`: Sample size
  - `W`: Time window (6)
  - `D`: Dimension (2D or 3D)
- **n_particles_per_example** (list): Integer `[1,]` indicating the size of the sample `N`
- **output** (list): Ground truth for predicted state `[N, D]`

#### `rollout.pt/rollout_full.pt`
- **position** (list): Contains a list of all trajectories, where each element corresponds to a complete trajectory with shape `[N, T, D]` where:
  - `N`: Number of particles
  - `T`: Rollout duration
  - `D`: Dimension (2D or 3D)

> **Note:** `particle_type`, `n_particles_per_example`, and `output` in `rollout.pt/rollout_full.pt` are **not relevant** and should be ignored.

### Metadata Files

Each dataset folder contains a `metadata.json` file with the following information:
- **bounds** (list): Boundary conditions.
- **default_connectivity_radius** (float): Radius used within the graph neural network.
- **vel_mean** (list): Mean velocity of the entire dataset `[x, y, (z)]` for noise profiling.
- **vel_std** (list): Standard deviation of velocity `[x, y, (z)]` for noise profiling.
- **acc_mean** (list): Mean acceleration `[x, y, (z)]` for noise profiling.
- **acc_std** (list): Standard deviation of acceleration `[x, y, (z)]` for noise profiling.

> **Note:** `sequence_length`, `dim`, and `dt` can be ignored.

## How to Use

### Example Usage

```python
from datasets import load_dataset

# Load the dataset from Hugging Face
dataset = load_dataset("hrishivish23/MPM-Verse-MaterialSim-Small", data_dir=".")
```

### Processing Examples

```python
import torch
import pickle

with open("path/to/train.obj", "rb") as f:
  data = pickle.load(f)

positions = data["position"][0]
print(positions.shape)  # Example output: (N, W, D)
```

## Citation

If you use this dataset, please cite:
```bibtex
@article{viswanath2024reduced,
  title={Reduced-Order Neural Operators: Learning Lagrangian Dynamics on Highly Sparse Graphs},
  author={Viswanath, Hrishikesh and Chang, Yue and Berner, Julius and Chen, Peter Yichen and Bera, Aniket},
  journal={arXiv preprint arXiv:2407.03925},
  year={2024}
}
```

## Source  
This dataset aggregates Material Point Method (MPM) simulations from two primary sources:  

- **2D Simulations**  
  - The 2D datasets (e.g., *Water2D, Sand2D, MultiMaterial2D*) are derived from [Sánchez-González et al. (ICML 2020)](https://proceedings.mlr.press/v119/sanchez-gonzalez20a.html), which introduced the use of **Graph Neural Networks (GNNs) for learning physics-based simulations**.  

- **3D Simulations**  
  - The 3D datasets (e.g., *Water3D, Sand3D, Plasticine3D, Jelly3D, RigidCollision3D, Melting3D*) were generated using the **NCLAW Simulator**, developed by [Ma et al. (ICML 2023)](https://proceedings.mlr.press/v202/ma23a.html).  

### Citations  
```bibtex
@inproceedings{sanchez2020learning,
  title={Learning to simulate complex physics with graph networks},
  author={Sanchez-Gonzalez, Alvaro and Godwin, Jonathan and Pfaff, Tobias and Ying, Rex and Leskovec, Jure and Battaglia, Peter},
  booktitle={International Conference on Machine Learning},
  pages={8459--8468},
  year={2020},
  organization={PMLR}
}

@inproceedings{ma2023learning,
  title={Learning neural constitutive laws from motion observations for generalizable pde dynamics},
  author={Ma, Pingchuan and Chen, Peter Yichen and Deng, Bolei and Tenenbaum, Joshua B and Du, Tao and Gan, Chuang and Matusik, Wojciech},
  booktitle={International Conference on Machine Learning},
  pages={23279--23300},
  year={2023},
  organization={PMLR}
}
```