giorom-3d-t-elasticity-3d

📌 PhysicsEngine: Reduced-Order Neural Operators for Lagrangian Dynamics

By Hrishikesh Viswanath, Yue Chang, Julius Berner, Peter Yichen Chen, Aniket Bera

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📝 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/Elasticity3DSmall,

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

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📊 Available Model Variants

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

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💡 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.

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🚀 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

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📂 Model Weights and Checkpoints

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📚 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

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📜 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}
}

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💬 Contact

For questions or collaborations:

• 🧑‍💻 Author: Hrishikesh Viswanath
• 📧 Email: [email protected]
• 💬 Hugging Face Discussion: Model Page

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🔗 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

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🔹 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).