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4 Qualifying Exam/4 Presentation/Outline.md

@@ -90,6 +90,106 @@ _(Include a visual of how $\Delta$ affects $P$)_
 # Goals and Outcomes
 
 # Research Methodology
+### **Slide 1: Research Motivation**
+
+**Assertion:** Current methods for generating unstructured perturbations are limited in flexibility and generalizability.
+
+- **Evidence:**
+    - Unstructured perturbations lack adaptability to various scenarios.
+    - Proposed approach leverages diffusion generative models for flexible perturbation generation.
+
+**Visuals:**
+
+- A flowchart contrasting traditional perturbation methods vs. diffusion models.
+
+---
+
+### **Slide 2: Diffusion Model Features**
+
+**Assertion:** Frequency response data forms the foundation for feature creation in diffusion models.
+
+- **Evidence:**
+    - Features discretize dynamics into a vector of magnitude and phase.
+    - Supports training without imparting unintended structure.
+
+**Visuals:**
+
+- Diagram from Figure 1 showing the discretization of frequency response.
+
+---
+
+### **Slide 3: Creating Frequency Features**
+
+**Assertion:** Discretizing the frequency response enables scalable feature sets.
+
+- **Evidence:**
+    - Fine resolution for complex behavior or coarse for computational efficiency.
+    - Features provide physical context across frequency scales.
+
+**Visuals:**
+
+- Table comparing fine vs. coarse frequency sampling.
+- Annotated example of magnitude/phase vector with scales labeled.
+
+---
+
+### **Slide 4: Training the Diffusion Model**
+
+**Assertion:** Diffusion models learn unstructured perturbations through iterative noise transformation.
+
+- **Evidence:**
+    - Forward process adds noise; reverse process removes it.
+    - Training maximizes log-likelihood between input and reconstructed data.
+
+**Visuals:**
+
+- Flowchart of the diffusion training process.
+- Key equations (e.g., Eq. \ref{forward_kernel} and \ref{reverse_kernel}) simplified with annotations.
+
+---
+
+### **Slide 5: Generating New Perturbations**
+
+**Assertion:** The trained diffusion model generates diverse and flexible perturbations.
+
+- **Evidence:**
+    - Outputs are probabilistic, enabling variability.
+    - Perturbation level controlled by adjusting time steps.
+
+**Visuals:**
+
+- Illustration of forward/reverse process with arrows and annotations.
+- Graph showing interpolation from partial time steps.
+
+---
+
+### **Slide 6: Ensuring Valid Perturbations**
+
+**Assertion:** Generated perturbations must meet robust control requirements.
+
+- **Evidence:**
+    - No additional right-hand plane poles.
+    - Supremum gain of Δ below threshold β.
+
+**Visuals:**
+
+- Diagram of pole-zero constraints.
+- Workflow for verifying Δ and fitting transfer functions.
+
+---
+
+### **Slide 7: Advantages of Diffusion Models**
+
+**Assertion:** Diffusion models provide a novel solution for generating unstructured perturbations.
+
+- **Evidence:**
+    - Introduce non-deterministic variability into perturbations.
+    - Overcome the limitations of traditional structured approaches.
+
+**Visuals:**
+
+- Comparative chart: structured vs. unstructured methods.
+- Examples of perturbed frequency responses generated by the model.
 # Metrics of Success
 # Risks and Contingencies
 #