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,

⚠ 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

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`
`giorom-3d-t-water3d`	`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
📧 Email: hviswan@purdue.edu
💬 Hugging Face Discussion: Model Page

🔗 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).

hrishivish23/giorom-3d-t-sand-3d

📌 PhysicsEngine: Reduced-Order Neural Operators for Lagrangian Dynamics

📝 Model Overview