Update README.md

README.md

@@ -68,4 +68,76 @@ biases:
 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."
+
+# 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 (if applicable)
+citation: |
+  @misc{neuraloperator_nns_to_nos,
+    author = {The Neural Operator Community},
+    title = {NNs-to-NOs: Neural Networks to Neural Operators},
+    howpublished = {\url{https://github.com/neuraloperator/NNs-to-NOs.git}},
+    year = {2023}
+  }
+  @misc{navier_stokes_2d_dataset,
+    author = {ajsbsd},
+    title = {Navier-Stokes 2D Dataset},
+    howpublished = {\url{https://huggingface.co/datasets/ajsbsd/navier-stokes-2d-dataset}},
+    year = {2023}
+  }
+---
+
+# Fine-Tuning This Neural Operator: A Simple Guide
+
+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.
+
+## What is Fine-Tuning?
+
+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.
+
+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.
+
+## Our Fine-Tuning Process
+
+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.
+
+Here's what happened:
+
+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.
+
+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.
+
+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.
+
+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.
+
+## Why This Matters
+
+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.
+
+Feel free to explore the model and its capabilities!