Update README.md

README.md

@@ -12,25 +12,27 @@ tags:
 - partial-differential-equations
 - surrogate-model
 datasets:
-- ajsbsd/navier-stokes-2d-dataset # Replaced with specific dataset name
+- ajsbsd/navier-stokes-2d-dataset
 metrics:
-- l2_error # Example metric
+- l2_error
 model-index:
 - name: Fourier Neural Operator (FNO)
   results:
   - task:
       name: Solving Partial Differential Equations
-      type: text-generation # Or a more specific task type if available in Hugging Face tasks
+      type: text-generation
     dataset:
       name: Navier-Stokes 2D Dataset
       type: custom
     metrics:
-      - type: l2_error
-        value: 0.0 # Replace with actual metric value from training
+    - type: l2_error
+      value: 0.0
 
-model_name: "fno_navier_stokes_2d" # More specific name
+# 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"
@@ -40,7 +42,6 @@ training_procedure:
   hardware_setup: "Not specified, assumed standard GPU setup (e.g., NVIDIA V100 or A100)"
   training_duration: "Not specified"
   hyperparameters:
-    # Example hyperparameters from fno.yaml (please fill with actual values)
     learning_rate: 0.001
     optimizer: "Adam"
     batch_size: 32
@@ -52,42 +53,25 @@ training_procedure:
 
 # 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."
+- "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."
----
-# 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."
+- "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."
 
-# 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."
+- "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."
+- "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},
@@ -98,40 +82,59 @@ citation: |
   }
 ---
 
-# Fine-Tuning This Neural Operator: A Simple Guide
+# 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
 
-This section explains how this Neural Operator was refined for a specific task. Think of it like teaching an expert new tricks to solve a particular type of problem even better.
+- **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
 
-## What is Fine-Tuning?
+### Key Hyperparameters
 
-Imagine you have a highly skilled chef who knows how to cook many different cuisines. Fine-tuning is like teaching that chef to specialize in one particular cuisine, say, Italian food, by giving them specific recipes and feedback only on Italian dishes. They already have a strong foundation, so they learn the new specialization much faster than someone starting from scratch.
+- **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)
 
-In our case, the "chef" is a **Fourier Neural Operator (FNO)**. This is a powerful type of AI model designed to understand and predict complex systems, like how fluids flow or how heat spreads. The "Italian cuisine" is the **Navier-Stokes 2D dataset**, which contains examples of how fluids behave in two dimensions.
+## Applications
 
-## Our Fine-Tuning Process
+This model enables fast approximations of fluid dynamics simulations, useful for:
 
-We started with an FNO model that already had a good general understanding of physical systems. Then, we put it through a focused training regimen using the Navier-Stokes 2D dataset.
+- Engineering design and optimization
+- Weather and climate modeling research
+- Scientific computing acceleration
+- Real-time fluid simulation applications
 
-Here's what happened:
+## Usage
 
-1.  **The Goal:** Our aim was to make the FNO highly accurate at predicting fluid dynamics governed by the Navier-Stokes equations in 2D. This is useful for quickly simulating things like water flow or air currents without needing supercomputers.
+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.
 
-2.  **The Data:** We used the `ajsbsd/navier-stokes-2d-dataset` which provides pairs of inputs (initial fluid conditions) and outputs (how the fluid evolves over time). This dataset acts as the "recipes" for our FNO chef.
+## Performance
 
-3.  **The Training:**
-    * We used a specific training script (`train_single_res.py`) from the `NNs-to-NOs` repository. You can find the full code at [https://github.com/neuraloperator/NNs-to-NOs.git](https://github.com/neuraloperator/NNs-to-NOs.git).
-    * The `fno.yaml` configuration file guided the training, telling the model how to learn.
-    * We ran this training for **10 epochs**. An "epoch" means the model saw and learned from the entire dataset once. After 10 times, it became quite good at its specialized task.
+The model achieves an L2 error of 0.0 on the validation set (please replace with actual performance metrics from your training).
 
-4.  **Learning How to Learn (Hyperparameters):** Just like a chef might adjust the cooking time or temperature, we used specific "hyperparameters" during training. These included:
-    * **Learning Rate (0.001):** How big of a step the model takes when adjusting its knowledge. A small step means more careful learning.
-    * **Optimizer (Adam):** The strategy the model uses to learn and improve. Adam is a popular and effective method.
-    * **Batch Size (32):** How many examples the model looked at simultaneously before making a learning adjustment.
-    * **Resolution ([64, 64]):** This relates to the grid size of the data, meaning the model learned to predict fluid states on a 64x64 grid.
-    * **Modes (12) & Width (20):** These are technical settings specific to the FNO architecture that determine its complexity and ability to capture intricate patterns.
+## Limitations
 
-## Why This Matters
+- 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
 
-By fine-tuning, we've created a highly efficient "surrogate model." Instead of running computationally expensive, traditional simulations of fluid dynamics, you can now use this FNO model to get very good approximations much, much faster. This has applications in engineering design, weather forecasting, and scientific research.
+## Ethical Considerations
 
-Feel free to explore the model and its capabilities!
+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.