🧪 Particle Event Simulation, Diffusion-Based Augmentation, and Classification

📌 Overview

This project presents an end-to-end physics-aware pipeline for simulating, augmenting, classifying, and generating particle detector events using deep learning.

The workflow closely mirrors real high-energy physics (HEP) analysis pipelines:

Physics-inspired simulation
        ↓
Class-conditioned diffusion (data augmentation)
        ↓
CNN / Vision Transformer classification
        ↓
Physics-consistent evaluation

The project is suitable for academic research, HEP ML coursework, and BE level experimentation.

---

🧩 Particle Classes

Class ID	Particle	Physical Meaning
0	Muon	Straight minimum-ionizing track
1	Electron	Compact electromagnetic shower
2	Hadron	Chaotic hadronic shower

---

🔬 Physics-Inspired Detector Simulation

Image Properties

• Resolution: 64 × 64
• Single-channel grayscale
• Gaussian blur + detector noise
• Normalized per image

Event Characteristics

🟢 Muon

• Straight-line trajectory
• Minimal lateral spread
• Low energy deposition

🔵 Electron

• Compact EM shower
• Radially symmetric
• Moderate energy

🔴 Hadron

• Multi-cluster structure
• Highly stochastic
• Large energy fluctuations

---

Dataset Preparation

Simulated samples in BW

Muon Samples

Hadron Samples

Electron Samples

---

🌫️ Diffusion-Based Event Generation (Before Classification)

Why Diffusion Comes First

In real experiments, Monte-Carlo generators produce large datasets before reconstruction or classification.

Here, a class-conditioned diffusion model (DDPM) acts as a learned Monte-Carlo generator, producing realistic detector events used to augment training data.

Model Details

• UNet-based DDPM (diffusers.UNet2DModel)
• Explicit class conditioning
• Noise scheduler: squaredcos_cap_v2

Energy Conservation

Generated events are rescaled to satisfy:

Class Target Energy

---

Muon 300 Electron 2000 Hadron 3500

This mimics calorimeter energy calibration.

---

🔬 Physics Interpretation of Generated Events

• Muons: Straight coherent tracks preserved by diffusion
• Electrons: Smooth compact showers with radial falloff
• Hadrons: Complex multi-cluster stochastic structures

Diffusion successfully captures class-specific topology and energy flow, making it suitable for physics-aware augmentation.

---

DDPM Generated samples in B/W

DDPM Augmentation

---

Final Combined Samples in B/W

DDPM Augmentation

---

🧠 Supervised Classification Models

CNN -- VGG16

• ImageNet pretrained backbone
• Frozen convolutional layers
• Custom classifier head
• Strong local inductive bias

Vision Transformer -- ViT-B/32

• Pretrained ViT encoder
• Global self-attention
• Better modeling of complex hadronic topology

---

Final Training Dataset

---

CNN (VGG16) Results

Accuracy Curve

Loss Curve

Confusion Matrix

Normalized Confusion Matrix

Precision–Recall Curve

ROC Curve

Sample Predictions

---

Vision Transformer (ViT) Results

Accuracy Curve

Loss Curve

Confusion Matrix

Normalized Confusion Matrix

Precision–Recall Curve

ROC Curve

Sample Predictions

---

---

📊 CNN vs Vision Transformer (Physics-Aware Comparison)

Conceptual Comparison

Aspect CNN (VGG16) ViT

---

Feature focus Local Global Physics analogy Local energy deposits Event-level topology Noise robustness Moderate High

Performance & Behavior

Criterion	CNN (VGG16)	ViT-B/32
Training stability	High	Medium
Muon classification	⭐⭐⭐⭐⭐	⭐⭐⭐⭐⭐
Electron classification	⭐⭐⭐⭐	⭐⭐⭐⭐⭐
Hadron classification	⭐⭐⭐	⭐⭐⭐⭐
Generalization	Moderate	Strong

Interpretation

• CNNs excel at localized structures (tracks, compact showers)
• ViTs excel at global reasoning (hadronic fragmentation)

---

🔁 Role of Diffusion in Classification

Diffusion-based augmentation: - Increases sample diversity - Reduces overfitting - Improves electron and hadron recognition

Diffusion augments, not replaces, physics simulation.

---

📦 Dependencies

torch
torchvision
diffusers
numpy
scikit-learn
matplotlib
seaborn
tqdm

---

🚀 Applications

• Particle identification
• Detector response modeling
• HEP ML research
• Data augmentation studies

---

👤 Author

Anurag G.C.
Computer Engineering
IOE Pulchowk Campus
Nepal 🇳🇵