hrishivish23/giorom-3d-t-plasticine-3d

📌 PhysicsEngine: Reduced-Order Neural Operators for Lagrangian Dynamics

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

📝 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/Plasticine3DNCLAWSmall`,

⚠ 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).

💡 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

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

import torch

📂 Model Weights and Checkpoints

📚 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:

@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).