---
license: mit
datasets:
- hrishivish23/MPM-Verse-MaterialSim-Small
- hrishivish23/MPM-Verse-MaterialSim-Large
language:
- en
metrics:
- accuracy
pipeline_tag: graph-ml
tags:
- physics
- scientific-ml
- lagrangian-dynamics
- neural-operator
- neural-operator-transformer
- graph-neural-networks
- graph-transformer
- sequence-to-sequence
- autoregressive
- temporal-dynamics
---

# 📌 PhysicsEngine: Reduced-Order Neural Operators for Lagrangian Dynamics

**By [Hrishikesh Viswanath](https://huggingface.co/hrishivish23), Yue Chang, Julius Berner, Peter Yichen Chen, Aniket Bera**  

![Physics Simulation](https://hrishikeshvish.github.io/projects/giorom_data/giorom_pipeline_plasticine.png)

---

## 📝 Model Overview  
**GIOROM** is a **Reduced-Order Neural Operator Transformer** designed for **Lagrangian dynamics simulations on highly sparse graphs**. The model enables hybrid **Eulerian-Lagrangian learning** by:  

- **Projecting Lagrangian inputs onto uniform grids** with a **Graph-Interaction-Operator**.  
- **Predicting acceleration from sparse velocity inputs** using past time windows with a **Neural Operator Transformer**.  
- **Learning physics from sparse inputs (n ≪ N)** while allowing reconstruction at arbitrarily dense resolutions via an **Integral Transform Model**.
- **Dataset Compatibility**: This model is compatible with [`MPM-Verse-MaterialSim-Small/Sand3DNCLAWSmall`](https://huggingface.co/datasets/hrishivish23/MPM-Verse-MaterialSim-Small/tree/main/Sand3DNCLAWSmall), 

⚠ **Note:** While the model can infer using an integral transform, **this repository only provides weights for the time-stepper model that predicts acceleration.**

---

## 📊 Available Model Variants  
Each variant corresponds to a specific dataset, showcasing the reduction in particle count (n: reduced-order, N: full-order).  

| Model Name                     | n (Reduced) | N (Full) |
|---------------------------------|------------|---------|
| `giorom-3d-t-sand3d-long`       | 3.0K       | 32K     |
| `giorom-3d-t-water3d`           | 1.7K       | 55K     |
| `giorom-3d-t-elasticity`        | 2.6K       | 78K     |
| `giorom-3d-t-plasticine`        | 1.1K       | 5K      |
| `giorom-2d-t-water`             | 0.12K      | 1K      |
| `giorom-2d-t-sand`              | 0.3K       | 2K      |
| `giorom-2d-t-jelly`             | 0.2K       | 1.9K    |
| `giorom-2d-t-multimaterial`     | 0.25K      | 2K      |

---

## 💡 How It Works  

### 🔹 Input Representation  
The model predicts **acceleration** from past velocity inputs:  

- **Input Shape:** `[n, D, W]`  
  - `n`: Number of particles (reduced-order, n ≪ N)  
  - `D`: Dimension (2D or 3D)  
  - `W`: Time window (past velocity states)  

- **Projected to a uniform latent space** of size `[c^D, D]` where:  
  - `c ∈ {8, 16, 32}`  
  - `n - δn ≤ c^D ≤ n + δn`  

This allows the model to generalize physics across different resolutions and discretizations.  

### 🔹 Prediction & Reconstruction  
- The model **learns physical dynamics** on the sparse input representation.  
- The **integral transform model** reconstructs dense outputs at arbitrary resolutions (not included in this repo).  
- Enables **highly efficient, scalable simulations** without requiring full-resolution training.

---

## 🚀 Usage Guide  
### 1️⃣ Install Dependencies
```bash
pip install transformers huggingface_hub torch
```
```
git clone https://github.com/HrishikeshVish/GIOROM/
cd GIOROM
```


### 2️⃣ Load a Model



```python
from models.giorom3d_T import PhysicsEngine
from models.config import TimeStepperConfig

time_stepper_config = TimeStepperConfig()

simulator = PhysicsEngine(time_stepper_config)
repo_id = "hrishivish23/giorom-3d-t-sand3d"
time_stepper_config = time_stepper_config.from_pretrained(repo_id)
simulator = simulator.from_pretrained(repo_id, config=time_stepper_config)
```

### 3️⃣ Run Inference
```python
import torch

```

---

## 📂 Model Weights and Checkpoints  
| Model Name                     | Model ID |
|---------------------------------|-------------|
| `giorom-3d-t-sand3d-long`            | [`hrishivish23/giorom-3d-t-sand3d-long`](https://huggingface.co/hrishivish23/giorom-3d-t-sand3d-long) |
| `giorom-3d-t-water3d`           | [`hrishivish23/giorom-3d-t-water3d`](https://huggingface.co/hrishivish23/giorom-3d-t-water3d) |


---

## 📚 Training Details  
### 🔧 Hyperparameters  
- **Graph Interaction Operator** layers: **4**
- **Transformer Heads**: **4**
- **Embedding Dimension:** **128**  
- **Latent Grid Sizes:** `{8×8, 16×16, 32×32}`  
- **Learning Rate:** `1e-4`  
- **Optimizer:** `Adamax`  
- **Loss Function:** `MSE + Physics Regularization (Loss computed on Euler integrated outputs)`  
- **Training Steps:** `1M+ steps`  

### 🖥️ Hardware  
- **Trained on:** NVIDIA RTX 3050
- **Batch Size:** `2`  

---

## 📜 Citation  
If you use this model, 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}
}
```

---

## 💬 Contact  
For questions or collaborations:  
- 🧑‍💻 Author: [Hrishikesh Viswanath](https://hrishikeshvish.github.io)  
- 📧 Email: hviswan@purdue.edu 
- 💬 Hugging Face Discussion: [Model Page](https://huggingface.co/hrishivish23/giorom-3d-t-sand3d-long/discussions)  

---

## 🔗 Related Work  
- **Neural Operators for PDEs**: Fourier Neural Operators, Graph Neural Operators  
- **Lagrangian Methods**: Material Point Methods, SPH, NCLAW, CROM, LiCROM
- **Physics-Based ML**: PINNs, GNS, MeshGraphNet

---

### 🔹 Summary  
This model is ideal for **fast and scalable physics simulations** where full-resolution computation is infeasible. The reduced-order approach allows **efficient learning on sparse inputs**, with the ability to **reconstruct dense outputs using an integral transform model (not included in this repo).**