# AI-Enabled Compact and Efficient Dynamic Light Scattering System for Precise Microparticle Sizing
## 3 Results and Discussion
The GAF is a mathematical transformation technique that converts a 1D time series or curve into a 2D representation [36], often visualized as a grayscale image or heatmap. This transformation allows the temporal patterns within the data to be preserved while enabling the use of image-based analytical methods, such as CNN, for feature extraction and analysis [37; 38]. The single-GAF recognition model is defined in Figure 3c, constructed using the sequential application programming interface (API), features two convolutional layers, each equipped with eight filters of size 3 \(\times\) 3 and ReLU activation functions, succeeded by MaxPooling layers with pool sizes of 10 \(\times\) 10. Following the flattening of pooled features, the model incorporates a dense layer comprising 128 neurons with ReLU activation and a dense layer comprising 64 neurons with ReLU activation. The output layer consists of a single neuron, tailored for predicting a continuous value in a regression task. As shown in Figure 3d, the process begins by normalizing the time series data to ensure that all values fall within the range of [\(-\)1, 1], which is crucial for angle-based encoding. Each data point in the normalized series is then represented as an angle in polar coordinates, where the value of the data determines the angle, and the temporal sequence defines the radius. Using this polar mapping, the cosine similarity between each  
Figure 3: Structures of the (**a**) DNN, (**b**) 1D-CNN, (**c**) single-GAF recognition, (**d**) GASE, and GADF as inputs for the single-GAF recognition model, and (**e**) the fusion of GASE and GADF models. pair of points in the series is computed to form a Gramian matrix. The resulting matrix encodes the temporal correlations and structural relationships within the time series, which are preserved in the two-dimensional (2D) representation. GAF is divided into Gramian angular summation field (GASF) and Gramian angular difference field (GADF), and their effects on different models also vary [39]. By transforming a one-dimensional (1D) time series into a 2D GASF/GADF, this method facilitates the application of advanced image processing techniques to time-domain data, enabling more effective feature extraction and improving model performance in tasks such as classification, regression, and clustering. Then, use the single-GAF recognition model in Figure 3c to take GADF and GASF as inputs, respectively. Figure 3e illustrates the utilization of these upscaled light intensity images for improving the single-GAF recognition model [37]. The method is to fuse GASF and GADF and input both images to the 2D-CNN network simultaneously [40]. Finally, the neurons of the two networks are connected in the fully connected layer and then passed through two layers of density to output the particle size result. Compiled with the Adam optimizer, the model employs the mean squared error (MSE) as the loss function and MAE as a supplementary metric [41]. This architectural design is optimized for capturing spatial features and delivering precise predictions. The ACF was selected as the input to the model, as it provides a condensed yet highly informative representation of the scattering signal [9, 11, 12]. Directly using the raw signal as input, while feasible, would significantly increase the computational burden and prolong training time, as demonstrated in Supplementary Figure S2. Notably, the training performance of models using the raw signal was not substantially better than those employing the ACF, further validating the suitability of the ACF as the model input. To preprocess the ACF data, the initial 2000 points of each signal were extracted and compressed to 200 points by averaging every 10 consecutive values, reducing dimensionality without compromising critical features. To enhance the diversity and robustness of the dataset, the original 80 ACF datasets were further augmented to 160 by introducing random perturbations.