Neural-Integrated Meshfree (NIM) Method: A differentiable programming-based hybrid solver

Paper1, Paper2

Overview

The neural integrated meshfree (NIM) method is a GPU-accelerated differentiable meshfree computational approach built on JAX. It is specifically designed for forward and inverse modeling of elastic and inelastic materials using particle-based simulations. This repository provides the data and code supporting the accompanying paper.

Requirements

Python libraries required:

• jax
• tqdm
• scipy
• jaxopt
• tqdm

Installation

To install the required Python libraries, run the following command:

pip install jax tqdm scipy jaxopt

Tutorial Examples

1D Hyperelasticity using V-NIM

Explore the 1D Hyperelasticity model using the V-NIM method provided below:

• Code for NIM/c

• Code for NIM/h

Forward modeling for time dependent problem (advection diffusion equation) using S-NIM

• Forward modeling

• More examples demonstrating the application of the NIM method, including operator learning, inverse identification, elastoplasticity modeling, and geophysical simulation under extreme loading, will be released soon. Stay tuned for updates!

Acknowledgements

Contributors: Honghui Du (Graduate student), QiZhi He (PI)

Citation

@article{du2024neural,
  title={Neural-Integrated Meshfree (NIM) Method: A differentiable programming-based hybrid solver for computational mechanics},
  author={Du, Honghui and He, QiZhi},
  journal={Computer Methods in Applied Mechanics and Engineering},
  volume={427},
  pages={117024},
  year={2024},
  publisher={Elsevier}
}

@article{du2024differentiable,
  title={Differentiable Neural-Integrated Meshfree Method for Forward and Inverse Modeling of Finite Strain Hyperelasticity},
  author={Du, Honghui and Guo, Binyao and He, QiZhi},
  journal={arXiv preprint arXiv:2407.11183},
  year={2024}
}