# AI-Enabled Compact and Efficient Dynamic Light Scattering System for Precise Microparticle Sizing
## 3 Results and Discussion
This augmentation strategy ensured a more comprehensive dataset for model training and improved the generalization capability of the deep learning framework. The dataset of 160 samples was split into 80% training data and 20% test data for model development. During model training, the validation set consistently accounted for 10% of the data. Min-Max Normalization was applied for the dataset for rescaling feature values to a fixed range, typically [0, 1]. Each 1 s segment was transformed into a 200 \(\times\) 200 grayscale image using the GADF and GASF techniques, resulting in a total of 640 images. These images were subsequently used for CNN-based training and analysis. Figure 4 provides a comprehensive comparative analysis of the training dynamics and predictive performance of the DNN, 1D-CNN, and 2D-CNN models. Notably, the 2D-CNN was evaluated with three distinct input representations--GASF, GADF, and a fusion of GASF and GADF--offering a detailed assessment of their suitability for scattering signal analysis. The training and validation loss curves for all models exhibit good convergence, with no noticeable signs of significant overfitting or underfitting during training. This suggests that the models are likely well calibrated. However, to further substantiate the absence of overfitting, subsequent analysis using metrics such as MAE will be conducted to provide a more rigorous evaluation of the models' generalization performance and robustness. In terms of convergence speed, the 2D-CNN demonstrates a marked advantage, reaching convergence within 400 epochs, compared to 800 epochs for the DNN and 1200 epochs for the 1D-CNN. This efficiency highlights the capacity of the 2D-CNN to rapidly extract meaningful patterns from its two-dimensional input representations. When evaluated on the test dataset, the 2D-CNN with fused GASF and GADF input (2D-CNN (fusion)) achieves the highest accuracy, with an MAE of 10 nm. The 2D-CNN with GADF  
input follows closely, achieving a 14 nm MAE, while the 1D-CNN exhibits a competitive MAE of 22 nm. The 2D-CNN with a GASF input and the DNN lags behind, with MAEs of 24 nm and significantly higher errors, respectively, reaffirming the limitations of fully connected architectures in capturing the complex dynamics of scattering signals. This hierarchy of performance is further substantiated by the determination coefficients \(R^{2}\), which quantify the models' ability to explain variance in the data [40]. The 2D-CNN (fusion) and 2D-CNN (GADF) achieve near-perfect \(R^{2}\) values of 0.99, underscoring their superior predictive precision. The 1D-CNN and 2D-CNN (GASF) follow with strong \(R^{2}\) values of 0.98, reflecting their robust, albeit slightly less optimal, capacity for variance explanation. Conversely, the DNN trails with an \(R^{2}\) of 0.96, highlighting its reduced generalization capability. These findings suggest that while both the 1D-CNN and 2D-CNN (GASF) effectively extract meaningful features, the fusion of GASF and GADF representations for the 2D-CNN facilitates a richer representation of spatial correlations, thereby driving superior performance. The error band analysis (the right column) cor  
Figure 4: Loss, \(R^{2}\), RMSE and MAE of the DNN, 1D-CNN, 2D-CNN (GADF), 2D-CNN (GASF), and 2D-CNN (fusion) models. roborates these results. The 2D-CNN (fusion) exhibits the most tightly distributed error bands along the diagonal, reflecting its exceptional consistency and accuracy. The 2D-CNN (GADF) follows closely, with slightly wider error bands, while the 1D-CNN demonstrates commendable performance, albeit with marginally larger deviations. The 2D-CNN (GASF) also performs well but exhibits slightly reduced precision. The error band provides a visual representation of the model's performance in predicting microparticle sizes. On the plot, both the horizontal and vertical axes represent particle size, and the closer a point falls to the diagonal line, the smaller the prediction error.