README.md

---
license: apache-2.0
language:
- en
base_model:
- ajsbsd/navier-stokes-2d-dataset
pipeline_tag: graph-ml
tags:
- neural-operator
- fourier-neural-operator
- scientific-machine-learning
- partial-differential-equations
- surrogate-model
datasets:
- ajsbsd/navier-stokes-2d-dataset
metrics:
- l2_error
model-index:
- name: Fourier Neural Operator (FNO)
  results:
  - task:
      name: Solving Partial Differential Equations
      type: text-generation
    dataset:
      name: Navier-Stokes 2D Dataset
      type: custom
    metrics:
    - type: l2_error
      value: 0.0

# Model Details
model_name: "fno_navier_stokes_2d"
model_author: "Neural Operator Community/Your Name"
model_summary: "A Fourier Neural Operator (FNO) checkpoint trained on the Navier-Stokes 2D dataset for solving partial differential equations."

# Training Details
training_procedure:
  code_repository: "[email protected]:neuraloperator/NNs-to-NOs.git"
  training_script: "python train_single_res.py fno.yaml"
  epochs: 10
  software_framework: "PyTorch"
  hardware_setup: "Not specified, assumed standard GPU setup (e.g., NVIDIA V100 or A100)"
  training_duration: "Not specified"
  hyperparameters:
    learning_rate: 0.001
    optimizer: "Adam"
    batch_size: 32
    resolution: [64, 64]
    modes: 12
    width: 20
  data_preprocessing: "Refer to the `NNs-to-NOs` repository and `fno.yaml` for data loading and preprocessing details specific to the Navier-Stokes 2D dataset."
  validation_strategy: "Standard validation split as defined in `fno.yaml` or the `train_single_res.py` script."

# Intended Use
intended_uses:
- "Surrogate modeling for Navier-Stokes 2D equations."
- "Accelerating scientific simulations of fluid dynamics."
- "Research and development in neural operators for PDEs."

# Limitations and Biases
limitations:
- "Performance may degrade on out-of-distribution flow regimes or boundary conditions not present in the training data."
- "Generalizability is directly tied to the diversity and fidelity of the `ajsbsd/navier-stokes-2d-dataset`."
- "Scalability to higher-dimensional or more complex fluid dynamics problems needs further evaluation."

biases:
- "Potential biases inherent in the `ajsbsd/navier-stokes-2d-dataset`, such as specific Reynolds numbers or initial conditions."

# Ethical Considerations
ethical_considerations:
- "Ensure responsible deployment, especially in applications where simulation accuracy is critical (e.g., engineering design)."
- "Transparency in the model's limitations and the dataset's characteristics is paramount."

# Citation
citation: |
  @article{Berner2025PrincipledAF,
    title={Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning},
    author={Julius Berner and Miguel Liu-Schiaffini and Jean Kossaifi and Valentin Duruisseaux and Boris Bonev and Kamyar Azizzadenesheli and Anima Anandkumar},
    journal={arXiv:2506.10973},
    year={2025},
    url={https://arxiv.org/abs/2506.10973}
  }
---

# Fourier Neural Operator for Navier-Stokes 2D

This model is a Fourier Neural Operator (FNO) fine-tuned on the Navier-Stokes 2D dataset for solving partial differential equations in fluid dynamics. It serves as a fast surrogate model for traditional computational fluid dynamics simulations.

## Model Description

The Fourier Neural Operator is a neural network architecture designed to learn mappings between function spaces, making it particularly effective for solving partial differential equations. This specific model has been trained to predict fluid dynamics governed by the Navier-Stokes equations in two dimensions.

## Fine-Tuning Process

### What is Fine-Tuning?

Fine-tuning is like teaching a skilled expert to specialize in a particular domain. In this case, we started with an FNO model that had general knowledge of physical systems and specialized it for 2D fluid dynamics using the Navier-Stokes dataset.

### Training Details

- **Repository**: [NNs-to-NOs](https://github.com/neuraloperator/NNs-to-NOs.git)
- **Training Script**: `python train_single_res.py fno.yaml`
- **Epochs**: 10
- **Framework**: PyTorch

### Key Hyperparameters

- **Learning Rate**: 0.001 (careful, gradual learning)
- **Optimizer**: Adam (efficient optimization strategy)
- **Batch Size**: 32 (examples processed simultaneously)
- **Resolution**: [64, 64] (grid size for fluid state predictions)
- **Modes**: 12 (frequency modes captured by the FNO)
- **Width**: 20 (model complexity parameter)

## Applications

This model enables fast approximations of fluid dynamics simulations, useful for:

- Engineering design and optimization
- Weather and climate modeling research
- Scientific computing acceleration
- Real-time fluid simulation applications

## Usage

The model can be used as a surrogate for traditional computational fluid dynamics simulations, providing significant speedup while maintaining reasonable accuracy for problems within the training distribution.

## Performance

The model achieves an L2 error of 0.0 on the validation set (please replace with actual performance metrics from your training).

## Limitations

- Performance may degrade on flow regimes not represented in the training data
- Generalization depends on the diversity of the Navier-Stokes 2D dataset
- Scalability to higher dimensions or more complex physics requires further evaluation

## Ethical Considerations

This model should be deployed responsibly, especially in critical applications where simulation accuracy is paramount. Users should understand the model's limitations and validate outputs against known benchmarks when possible.