Update README.md

README.md

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----
-license: mit
----
+---
+license: mit
+language:
+- en
+tags:
+- physics
+- PDEs
+- surrogate
+- heat-equation
+- diffusion
+base_model: thuerey-group/pde-transformer
+---
+
+# PDE-Transformer mc-s – 2D Diffusion (Heat Equation) Fine-Tuned
+
+This repository provides a **fine-tuned version of PDE-Transformer (mc-s)** specialized for
+2D heat diffusion on regular grids. The base model is the mixed-channel small variant
+from `thuerey-group/pde-transformer`, further trained on synthetic solutions of the
+2D diffusion / heat equation with Gaussian bump initial conditions.
+
+The goal of this model is to act as a **surrogate solver** for short-time predictions
+of the heat equation, given a pair of previous states.
+
+> **Input:** 2-channel field `[u(t0), u(t1)]`  
+> **Output:** next-step prediction `u(t2)` (via channel index 1 in the model output)
+
+---
+
+## 🌐 Project Links
+
+- **Fine-tuning scripts & experiments**: [https://github.com/psmteja/agentic_ai_PDE_fm](https://github.com/psmteja/agentic_ai_PDE_fm)
+
+---
+
+## 📝 Model Description
+
+PDE-Transformer is a transformer-based foundation model for physics simulations on regular grids.
+It combines architectural ideas from diffusion transformers with design choices tailored to
+large-scale physical simulations.
+
+This checkpoint starts from the **mixed-channel small (mc-s)** variant and is **fine-tuned only on 2D diffusion**:
+
+- Equation:  
+  \[
+  \partial_t u = \nu (u_{xx} + u_{yy})
+  \]
+- Domain: \([-1, 1]^2\) discretized on a regular grid (e.g. \(64 \times 64\))
+- Boundary conditions: periodic
+- Initial condition: random 2D Gaussian bumps (random center, width, amplitude)
+- Training target: finite-difference solution `u(t2)` given `[u(t0), u(t1)]`
+
+### What this model is good for
+
+- Fast surrogate for **2D heat equation rollouts** over short time horizons.
+- Experiments in:
+  - surrogate modeling,
+  - model-based control for diffusion-like processes,
+  - benchmarking PDE foundation models on simple physics.
+
+### What this model is *not* guaranteed to handle
+
+- Arbitrary PDEs outside diffusion (e.g. Navier–Stokes, Burgers, reaction–diffusion)  
+  → use the original foundation model or fine-tune separately.
+- Very different resolutions or domain geometries than used during training,
+  unless you explicitly adapt / re-fine-tune.
+
+---
+
+## 📦 Installation
+
+Install the PDE-Transformer package and dependencies:
+
+```bash
+pip install pdetransformer torch numpy matplotlib