NeuralOperator

NeuralOperator is

• An educational Neural Operator library. The goal is to provide students with a light-weighted code to explore this area and interactive lectures with amazing Jupyter Notebook.
• A benchmark repository originally designed to test point cloud neural operator (PCNO) and other neural operators. The goal is to provide researchers with access to various parametric partial differential equations and associated datasets, enabling researchers to quickly and easily develop and test novel surrogate models.

Code Structure

• Utilities for all neural networks, such as optimizers and normalizers are in the utility folder.
• State-of-the-art neural operators, including fno.py, are in the baselines folder.
• The Point Cloud Neural Operator (PCNO), Multiscale Point Cloud Neural Operator (MPCNO), and their related utility files are in the pcno folder. If you plan to design a new neural operator, consider starting a dedicated folder similar to pcno.
• Datasets should be downloaded into the data folder. Each subfolder contains one dataset, such as darcy_square for the Darcy flow problem in the unit square.
• Test scripts are in the scripts folder. Each subfolder contains scripts for various neural operators applied to a specific dataset, with the folder name matching the corresponding dataset subfolder in the data folder.

NeuralOperator/

├── utility/
│   ├── adam.py
│   ├── losses.py
│   ├── normalizer.py

├── baselines/
│   ├── (various state-of-the-art neural operators, such as fno.py)

├── pcno/
│   ├── pcno.py
|   ├── mpcno.py
│   ├── geo_utility.py

├── tests/
│   ├── __init__.py
│   ├── (various test files, such as pcno_test.py)

├── data/
│   ├── (various data folders, such as darcy_square)

├── scripts/
│   ├── (various test script folders, such as darcy_square)

Tutorial

Let's start! (⚠️ under construction)

• Overview
  • Surrogate Modeling
  • Python Naming Conventions
• Neural operator
  • Fourier Neural Operator
  • Point Cloud Neural Operator
  • Multiscale Point Cloud Neural Operator
• Example
  • Advection-Diffusion Boundary Value Problem
    Focus: Adaptive meshing, Boundary layers, Different meshing strategies
  • Darcy Flow Problem on Square Domain
    Focus: Benchmark, Different mesh resolutions, Restart training
  • Darcy Flow Problem on Deformed Domain
    Focus: Different mesh resolutions, Variable geometries
  • Airfoil
    Focus: Benchmark, Discontinuities (Shock wave)
  • Airfoil with Flap
    Focus: Adaptive meshing, Topology variations, Discontinuities (Shock wave)
  • ShapeNet Car
    Focus: Benchmark, Three-dimensional
  • Ahmed Body
    Focus: Benchmark, Three-dimensional, Large-scale
  • Parachute Dynamics
    Focus: Three-dimensional, Unsteady problem
  • Curve Integral
    Focus: Singular kernel integrals, Geometric generalization
  • Mixed 3d
    Focus: Three-dimensional, Parallelization

Submit an issue

You are welcome to submit an issue for any questions related to NeuralOperator.

Here are some research papers using NeuralOperator

1. Chenyu Zeng, Yanshu Zhang, Jiayi Zhou, Yuhan Wang, Zilin Wang, Yuhao Liu, Lei Wu, Daniel Zhengyu Huang, "Point Cloud Neural Operator for Parametric PDEs on Complex and Variable Geometries."
2. Mingyu Han, Daniel Zhengyu Huang, Yuhan Wang, Yanshu Zhang, Jiayi Zhou, "Geometric Generalization of Neural Operators from Kernel Integral Perspective."