diff --git a/4 Qualifying Exam/4 Presentation/Outline.md b/4 Qualifying Exam/4 Presentation/Outline.md index 8d344054..20b5e11f 100644 --- a/4 Qualifying Exam/4 Presentation/Outline.md +++ b/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 # \ No newline at end of file