## 4 Methodology
### The Workflow for Real-Time UI/UX Adaptation in AI-MDD-UX
#### 4.3.4 GAN-Based UI Generation  
The GAN-based UI generation model enhances user experience by generating personalized and context-aware design. It dynamically adjusts the layout structure, component positioning and visual features to align with user preferences and behavior. To automate UI generation, the model processes persona embeddings and user interactions, generating UI layouts that make interactions more intuitive and engaging. Beyond the GAN model, the system **includes a generator that uses** embedded persona and user interaction to generate UI layouts. Additionally, a discriminator evaluates the authenticity of the generated UI against a training set of real UI components, ensuing UI remains personalized and aligned with the user's engagement level. The primary objectives of GANs in UI adaption are to:  
* Automate UI creation and generate diverse variations from historical user data, enabling faster prototyping, and adaptation to user needs. * Adjust UI layouts, colors, and element placements based on real-time interaction data, ensuring and optimized user experience without human intervention. * Generate personalized UI designs by training on engagement metrics such as clicks, time spent, and conversion rates. * Ensure visual appealing and functional UI layouts that enhance engagement. Figure 4 shows the architecture of GAN for UI generation. It consists in two-network architecture: (1) Generator (G), which takes user interaction data as input and generates a new UI layout by proposing adjustments to UI components that aligns with user preferences, (2) Discriminator (D), which evaluates the usability of the generated UI, determines whether the layout matches high-performing UI examples and provides feedback to refine the generator's output. The UI generation process begins by initializing generator (G) and discriminator (D) networks with random weights. The generator synthesizes UI layouts by processing three key inputs: (1) persona embeddings \(P_{u}\), (2) interaction feature vectors \(X_{u}\), and (3) a random noise vector \(x\sim\mathcal{N}(0,1)\) to ensuring diversity. The generation process is formally expressed as:  
\[\widehat{UI}=G(P_{u},X_{u},x). \tag{10}\]  
The discriminator then evaluates both generated and real historical UIs, assigning authenticity probabilities:  
\[D(UI)\rightarrow[0,1]\;\;D\Big{(}\widehat{UI}\Big{)}\rightarrow[0,1], \tag{11}\]  
where  
* \(D(UI)\): Probability a real \(UI\) is correctly identified. * \(D\Big{(}\widehat{UI}\Big{)}\): Probability a generated \(\widehat{UI}\) is misclassified as real. A higher value of \(D(UI)\) close to 1 indicates successful real UI recognition. A lower value of \(D\Big{(}\widehat{UI}\Big{)}\) close to 0 shows effective fake UI detection. As depicted in Algorithm 2, the training process involves an adversarial competition between the generator and discriminator networks, using both real historical UI layouts and artificially generated ones. The discriminator's goal is its ability to distinguish between real and generated layouts by widening the gap in their probability scores, while the generator progressively enhances its output quality to produce more convincing UI designs that can  
Figure 4: GAN-based UI generation architecture. deceive the discriminator. This adversarial dynamic is captured by the min-max objective function: \[L\underset{G}{\text{minmax}}\mathbb{E}_{UI\sim\widetilde{UI}}[\log D(UI)]+ \mathbb{E}_{x\sim P_{x}}[\log D(1-D(G(P_{u},X_{u},\varkappa)))],\] (12) where - \(\mathbb{E}_{UI\sim\widetilde{UI}}[\log D(UI)]\) drives the discriminator to accurately identify genuine UI layouts. - \(\mathbb{E}_{x\sim P_{x}}[\log D(1-D(G(P_{u},X_{u},\varkappa)))]\) pushes the generator to create outputs that the discriminator will incorrectly classify as authentic.