# AI-Enabled Compact and Efficient Dynamic Light Scattering System for Precise Microparticle Sizing
## 3 Results and Discussion
This diagonal line represents perfect agreement between the predicted and true sizes, serving as an ideal benchmark. The width of the error band around this line indicates the magnitude of deviation or uncertainty in the model's predictions. In contrast, the DNN displays the widest error bands and the least alignment along the diagonal, emphasizing its limitations in predictive accuracy. The differences observed in model behavior and performance can be explained by the principles of DL. The 1D-CNN excels at capturing temporal dependencies and localized patterns in the 1D ACF data, offering a compelling balance between accuracy and computational efficiency. In contrast, the 2D-CNN leverages the spatial correlations embedded in the GAF representations, particularly in its fusion of GASF and GADF inputs, enabling the extraction of higher-order features that underpin its superior precision. However, this advantage comes with increased computational demands, which may constrain its utility in applications requiring rapid inference or limited resources. The DNN's relatively poor performance underscores its lack of inductive bias for handling sequential or spatial data, resulting in suboptimal feature extraction and reduced generalization. Figure 5a-e display the ACFs for five repeated measurements of particle diameters at 100, 500, 700, 1000, and 1500 nm, respectively. The standard deviation (Std) of the five measurements for each diameter was calculated by converting the ACF curves into single values using the Frobenius norm (F) [42], with the results shown in the figures. The low variation observed is attributed to the noise from the simplified configuration and low-cost components of the AI-DLS system. PCA (Principal Component Analysis) is a statistical technique used primarily for data dimensionality reduction. It involves transforming a set of possibly correlated variables into a set of linearly uncorrelated variables, known as principal components. Despite this noise, the ACFs for different diameters remain distinct, as validated by PCA analysis, which successfully separates the ACFs for each diameter (Figure 5f). The dimensionality reduction data of PCA is used to reveal that although the ACF curve appears to have poor repeatability, there are still certain differences between data of different sizes after dimensionality reduction, thus proving that machine learning methods can separate noise, from ACF signals. After inputting the ACFs into the 2D-CNN (fusion) model (Figure 5g), the predicted diameters exhibited Std/errors of 3.75 nm/0.87%, 10.17 nm/0.68%, 7.94 nm/0.24%, 15.25 nm/0.54%, and 18.29 nm/0.81% for 100, 500, 700, 1000, and 1500 nm, respectively. The errors across repeated measurements remained below 1%, meeting the stringent repeatability standards of commercial DLS instruments. The robustness of the DL model against noise and variation explains the high stability of its predictions, outperforming conventional Stokes-Einstein equation-based methods in this regard. In particular, this study underscores the limitations of traditional methodologies that rely on the Stokes-Einstein equation, which predominantly extracts particle size information through signal matching. These conventional approaches are highly susceptible to noise interference and variations in signal quality, often arising from the constraints of low-cost instrumentation, thereby resulting in pronounced fluctuations in the final outcomes. By contrast, the proposed AI-DLS model demonstrates remarkable robustness, accurately predicting particle size information even under conditions where ACF signals are significantly degraded by noise. Figure 5h compares particle size measurements across  
the 100-1500 nm range between the AI-DLS system and a commercial instrument, using SEM-derived particle sizes as a reference. The results demonstrate excellent agreement between the two systems, with the AI-DLS system achieving reliability and accuracy comparable to its commercial counterpart.