Neural Network Enabled Real‐Time Plasma Imaging for Inverse Designed Fabrication of Micro/Nano Structures with Ultrafast Laser

ABSTRACT

Real‐time monitoring is essential for quality control in highprecision micro/nano structure fabrication with ultrafast laser. The laser‐induced plasma plume blocks the sample surface, preventing direct imaging of micro/nano structures during processing. This work proposes a neural networkenabled real‐time plasma imaging strategy and inverse design micro/nano fabrication method. The neural networks contain a conditional generative adversarial network (cGAN) for real‐time imaging and a multilayer perceptron (MLP) for inverse‐designed fabrication. Based on the fabrication of coffee‐ring feature structures, the cGAN generates high‐fidelity feature structure images from plasma intensity profiles, with a real‐time imaging latency of 1691 milliseconds. To validate the real‐time imaging strategy, dual‐pulse processing and sequential single‐pulse processing experiments are conducted across different materials. The MLP model establishes nonlinear relationships between laser parameters and feature structure size for inverse‐designed fabrication. Both forward prediction and inverse design results achieved a coefficient of determination (R²) of 0.97, and the actual fabrication results align with the target values. This work provides a neural networkenabled strategy for real‐time process monitoring, advancing the development of intelligent laser fabrication.

A neural networkenabled real‐time plasma imaging strategy and inverse design micro/nano fabrication method are proposed. The neural networks contain a conditional generative adversarial network (cGAN) for real‐time imaging and a multilayer perceptron (MLP) for inverse‐designed fabrication. The cGAN generates high‐fidelity feature structure images from plasma intensity profiles, advancing the development of intelligent laser fabrication.

1. Introduction

Ultrafast laser processing is an advanced fabrication technology. Over the past several decades, its scientific, technological, and industrial potential has been demonstrated [1, 2, 3]. This technique has several advantages, including mask‐free operation, high spatial resolution, and minimal thermal damage to the surrounding material [4, 5]. These characteristics have led to the widespread adoption of ultrafast laser for the fabrication of complex micro/nano structures, which give new functional properties to materials [6, 7] For instance, multi‐beam ultrafast laser lithography enables the fabrication of photonic crystals, which are designed to manipulate light propagation in the visible and near‐infrared ranges [8]. Laser‐induced solid‐liquid transitions can be utilized to generate coffee‐ring structures for large‐scale, high‐resolution color printing [9]. Ultrafast laser plasmonic fabrication can assemble metal nanocrystals into interconnected pattern networks, resulting in functional nanostructures with enhanced optical absorption and photothermal capacity [10]. Micro/nano structures are essential for advanced electronics, sensors, energy devices, and medicine [11, 12].

The quality of laser‐induced micro/nanostructures depends on several process parameters, including energy density, wavelength, pulse number, material properties, and polarization [13]. Excessive laser power or exposure time can lead to sample damage, and variations in beam position or shape impact machining precision [14, 15]. Parameter adjustment and quality control can be realized based on real‐time monitoring, which is essential for laser fabrication. Recent studies have demonstrated the use of snapshot compressive microscopy to monitor the development of self‐organized nanograting structures [16]. Optical coherence tomography enables in‐process depth measurements of structures formed by a femtosecond laser [17]. The laser‐induced plasma plume generated during processing blocks the sample surface, preventing direct imaging of micro/nano structures [18]. Previous studies have demonstrated the correlation between plasma plume characteristics and the process results in laser fabrication. The intensity regimes and length of plasma plume depend on the number of incident laser pulses [19]. Laser fluence affects the plasma expansion velocity [18]. These findings suggest that the plasma plume can serve as an indirect data source for imaging the sample surface during fabrication [20, 21].

Traditional process development in laser fabrication relies on iterative trial‐and‐error experiments [22]. Laser parameters are repeatedly adjusted based on post‐fabrication characterization results, such as scanning electron microscopy (SEM) images. This approach is inefficient and limits the speed of process development. With the development and applications of artificial intelligence, machine learning has been widely applied to predict processing outcomes and realize inverse design of laser parameters [23, 24]. Recent research demonstrates the effectiveness of machine learning across various manufacturing scenarios [25]. For instance, conditional generative adversarial networks (cGANs) have been used to generate surface morphology in pulse laser ablation and to visualize laser drilling processes [26, 27]. In the field of additive manufacturing, convolutional neural networks (CNNs) enable real‐time detection of porosity during laser powder bed fusion (LPBF) [28]. Neural network models can be used to establish quantitative mappings between laser processing parameters and the processing results [29, 30]. A tandem multilayer perceptron (MLP) has realized inverse design of photonic surfaces in high‐throughput femtosecond laser processing [31], and has achieved color prediction in laser‐induced thin films, which, combined with physics information [32]. These studies validate the potential of machine learning in realizing data‐driven process control and performance prediction for laser manufacturing. However, most studies focus on mapping input parameters to final performance metrics, neglecting the real‐time monitoring during processing. Various monitoring techniques have been developed, but active parameter optimization is required to achieve autonomous quality control. Integrating visual prediction with inverse‐designed fabrication is essential for intelligent laser fabrication systems.

In this work, we develop a neural networkenabled real‐time plasma imaging strategy for ultrafast laser processing to achieve inverse‐designed fabrication by combining two different neural network models. A cGAN model is used to realize process monitoring based on plasma observation. The cGAN model utilizes adversarial training to generate surface morphologies from plasma plume images, enabling real‐time imaging during laser fabrication. Dual‐pulse processing coffee‐ring and sequential single‐pulse processing experiments are conducted across different materials to validate the real‐time imaging strategy. The MLP model establishes the nonlinear relationship between laser power, dual‐pulse delay time (τ_d), and resulting inner/outer diameters of the coffee‐ring structures. The required laser parameters can be predicted based on target structural size, achieving the inverse‐designed fabrication.

2. Results and Discussion

The neural networkenabled real‐time imaging strategy for inverse‐designed fabrication proposed in this work is illustrated in Figure 1, which combines two machine learning models: a cGAN model for real‐time imaging of micro/nano feature structure and a multilayer perceptron (MLP) for inverse design of laser parameters. The cGAN is realized by the pix2pixHD model to translate plasma images into images of micro/nano feature structures [33]. The model includes a coarse‐to‐fine generator (Figure 1a), and a multi‐scale discriminator system. The generator contains two sub‐networks, the global generator network (G₂, blue and red blocks) and local enhancer networks (G₁, white blocks), respectively. Feature structure images can be generated through the synergy of G₁ and G₂. The discriminators can assess the realism of the generated images at different resolutions, compelling the generator through adversarial training to produce outputs that are both globally coherent and rich in fine detail. Figure 1b shows the plasma plume observation device, intensified charge coupled device (ICCD) camera is used to acquire plasma plume images. The laser pulses are focused onto the surface of the sample using a 5× objective, and the plasma plume induced by laser pulses is collected using a 10× objective.

FIGURE 1.

Schematic of neural networkenabled real‐time plasma imaging strategy to achieve inverse‐designed fabrication in ultrafast laser processing. (a) The generator structure of the cGAN. (b) Schematic diagram of the plasma plume observation device. (c) The forward and inverse MLP that used for establishing the nonlinear mapping relationships between laser parameters and feature structure diameters, the scale bar is 5 µm.

As shown in Figure 1c, the forward MLP model is designed to predict the inner and outer diameters (R_i and R_o) of the coffee‐ring structures from the laser processing parameters. Its network architecture consisted of an input layer for two variables (laser power, delay time), three hidden layers with 32, 64, and 32 neurons, respectively, and the output layer producing continuous values (inner, outer diameters). The Rectified Linear Unit (ReLU) is used as the activation function for the hidden layers, while a Linear activation function is used for the output layer. The inverse MLP features the same hidden layers as the forward MLP but with reversed input and output layers. It was developed for on‐demand fabrication. The inverse model takes the target diameters as inputs to design the required laser power and delay time. The cGAN and inverse MLP can work collaboratively. Real‐time plasma plume images are processed by cGAN to generate the surface morphology. The relevant geometric features (inner and outer diameters) can be extracted from generated or real images. These extracted sizes serve as inputs for the MLP model, which determines the laser power and delay time required for fabrication. In this work, we conduct many group experiments with different sets of laser parameters to collect experimental data (plasma plume images and coffee‐ring feature structures images) for the training of neural network models.

The partial experimental parameters and imaging results of cGAN are presented in Figure 2. Figure 2a shows the schematic of the experimental system, which includes both the dual pulse processing optical path and the imaging system based on a plasma plume observation device. In the optical path, michelson interference structure with a delay line is used to generate a dual pulse. The plasma plume images collected by the ICCD camera are input into the cGAN to generate feature structure images after processing. In the real‐time implementation, the cGAN network parameters are frozen after completion of training, and the model is deployed on a system equipped with an NVIDIA GeForce RTX 3050 Laptop GPU to achieve automated real‐time imaging. The experimental setup consists of two laptops: one that interfaces with the ICCD camera for plasma plume acquisition, and the other applied to run the cGAN inference. Once the plasma plume images are captured and stored, the cGAN model immediately processed the data to generate the corresponding feature structures. The demonstration of real‐time imaging is presented in Video S1. The total latency of the imaging system is 1691 ms, which is defined as the interval between image storage and result visualization. A breakdown of the processing time reveals that data preprocessing, cGAN inference, and result postprocessing account for 53, 1593, and 45 ms, respectively. The long inference time is attributed to the use of a complex model designed to generate sufficiently clear micro/nano feature structures. For the applications with high frequencies of ultrafast lasers, the total delay of this method can be reduced by utilizing higher‐performance industrial GPUs or appropriately optimizing the neural network architecture. It should be noted that this approach relies on large datasets and requires further optimization in imaging latency. The advantages of the proposed neural networkenabled real‐time imaging strategy include that it does not require complex optical paths or prior physical knowledge. This method uses plasma plume signals generated during laser processing, which is different from existing optical monitoring methods such as optical coherence tomography (OCT) [17].

FIGURE 2.

Dual‐pulse laser processing and cGAN training performance. (a) Schematic diagram of the dual‐pulse delay processing optical path and imaging system. (b) Schematic diagram of dual pulse processing for coffee‐ring structure. (c) The change in the coffee‐ring feature structure images generated by the neural network model with the number of training epochs. (d) cGAN training losses with FID score over epochs, original (gray) and smoothed (colored) curves for D_real, D_fake, and G_GAN losses.

Figure 2b illustrates the concept of dual pulse processing for fabricating coffee‐ring feature structures. The inner and outer diameters of these structures can be changed by adjusting the temporal separation (τ_d) between the dual pulses, which is precisely controlled by the mirror position on the delay line. Figure 2c offers a qualitative comparison of the generated feature structure images at different training epochs (from 20 to 200), demonstrating the improvement of image fidelity generated by cGAN with the improvement of training epochs. Figure 2d provides a quantitative evaluation of the performance of the model, the smoothed losses (original curve is gray) for the generator (G_GAN) and discriminator (D_real, D_fake) alongside with Fréchet Inception Distance (FID) score are shown. The reason for smoothing the loss curve is due to the inherent instability during the GAN model training process [34]. G_GAN represents the loss of the generator, quantifying how well its generated images can “fool” the discriminator into classifying them as “real”. D_real and D_fake represent the judgment errors of the discriminator on real images and generated images, respectively. The consistent decrease in G_GAN indicates that the generator progressively learned to produce more realistic images. The D_real and D_fake losses stabilized at 0.4–0.5, suggesting a balanced training dynamic where the discriminator cannot differentiate between real and generator‐produced images. The FID score is used to measure the similarity between the real and generated image, its steady decrease over training epochs also confirms the improvement in the realism of generated images.

The performance of cGAN on the testing dataset is presented in Figure 3, across laser powers of 3–13 mW and delay times of 30–70 ps. Figure 3a provides a qualitative comparison between real and generated images, using 8 representative subsets as examples. Each row displays: (1) the input plasma plume images, (2) the generated coffee‐ring feature structure images by cGAN, (3) the real feature structure images obtained by SEM, (4) the real feature structure images obtained by optical microscopy for visual comparison. The original plasma plume images collected by the ICCD camera are presented in Figure S1. The generated images show visual consistency with the actual SEM images of micro/nano structures. The sharp edges of the inner and outer rings images generated by the model can be clearly distinguished. Furthermore, we conduct several machine learning experiments with different feature structure images, finding that the clarity of training images significantly affected the fidelity of generated images (Figure S3).

FIGURE 3.

Generation results of cGAN on the testing dataset. (a) Some images of plasma plume during laser processing and the corresponded real/generated coffee‐ring feature structure, the scale bar is 5 µm. (b–g) Real and generated coffee‐ring feature structure diameter distribution corresponding to different processing parameters. Real outer diameters (b), Generated outer diameters (c), Difference in outer diameters (d), Real inner diameters (e), Generated inner diameters (f), Difference in inner diameters (g). (h) Statistical distribution of absolute prediction errors for the outer diameter, inner diameter, and ring width across the test dataset.

To quantitatively evaluate the fidelity of the generated image, the diameters of the coffee‐ring are measured from images and analyzed across the parameter space, as shown in heatmap in Figure 3b–g. (Partial data not included in the test dataset are interpolated from existing values to ensure the completeness of the heatmap.) Real inner and outer diameters distribution are shown in Figure 3b,e, respectively. Corresponding generated diameter distributions are shown in Figure 3c,f. Visual correlation in the color pattern and trends between real and generated is evident, indicating that the cGAN captured how the diameter changes with varying laser parameters. Furthermore, the fidelity of the generated images can be confirmed by the error distribution heatmap. The difference distribution of outer diameter (Figure 3d) and inner diameter (Figure 3g) between real and generated images is presented. The predominantly low values in the error distribution heatmap (indicated by dark blue) confirmed the generation error is minor across the entire tested range. These quantitative results validate the generation fidelity of the cGAN. To quantitatively evaluate the predictive accuracy of the real‐time imaging strategy, the statistical distribution of prediction errors across the test dataset is presented as a box plot in Figure 3h. For 75% of the test data, the absolute prediction errors for the outer diameter, inner diameter, and ring width (the difference between inner and outer diameters) are below 1 µm. The mean absolute error (MAE) and average relative error (ARE) for these parameters are shown in Table S1. The MAE values for the outer diameter, inner diameter, and ring width are 0.682, 0.490, and 0.619 µm, respectively. The corresponding ARE values are 5.40%, 5.29%, and 9.53%. These quantitative results confirm the accuracy of the real‐time imaging strategy.

The evaluation of the generation capability of the real‐time plasma strategy during sequential single‐pulse laser processing of silicon is presented in Figure 4. Figure 4a illustrates the architecture of cGAN for generating surface morphology after each individual laser pulse. The cGAN model processes each plasma plume image, which is captured during consecutive five laser pulses at the same processing location, and independently generates the corresponding surface morphology image. The generator contains a global generator network (G₁) and a local enhancement network (G₂). The downsampled version of the plasma plume image is input to G₁, while the original image is input to the front end of G₂ (G₂ ^(F)). Specifically, both G₁ and G₂ contain a convolutional front‐end G^(F), a set of residual blocks G^(R), and a transposed convolutional back‐end G^(B), respectively. The feature map output from G₁ ^(B) is added to the feature map from G₂ ^(F), and the combined map is processed by the residual block (G₂ ^(R)) and the back end of G₂ (G₂ ^(B)) to finally generate the processed surface morphology images. The realism of the generated images is optimized by adversarial training between the discriminator and generator. The discriminator comprises three structurally identical sub‐discriminators, each containing five convolutional layers. The sub‐discriminator is applied to the original image or its downsampled versions, respectively. This architecture allows the discriminator to simultaneously capture global consistency and local details of generated images at different scales. During training, the total loss function is the sum of the losses from the three sub‐discriminators, optimizing the discrimination weight parameters.

FIGURE 4.

The generalization of real‐time plasma imaging strategy in sequential single pulse processing. (a) cGAN for generating temporal pulse processing, the scale bar is 5 µm. (b) Some images of plasma plume during laser processing and the corresponding real processed morphology, and the generated processed morphology, the scale bar is 5 µm. (c) Training losses with FID score over epochs, original (gray) and smoothed (colored) curves for D_real, D_fake, and G_GAN losses.

The generation accuracy of cGAN is qualitatively demonstrated in Figure 4b, which displays eight representative examples. The generated morphology (second column) is similar to the real morphology observed experimentally (third column), validating the effectiveness of cGAN across different materials. The original plasma plume images collected by the ICCD camera are presented in Figure S4. To quantitatively evaluate the performance of cGAN, Figure 4c presents the dynamics results during training, including the loss curves and the FID score. The smoothed losses for the discriminator (red and blue curves) rapidly stabilize at a fixed value (approximately 0.4 for D_real and D_fake). This indicates that a training equilibrium has been achieved, where the discriminator is effective but not overpowering. The smoothed loss of the generator shows a consistent downward trend, confirming that the generator is progressively improving its ability to produce more realistic images. Furthermore, the FID score shows a steady decrease over the 200 epochs. These results prove that the cGAN model can generate surface morphology under sequential single pulse processing conditions, demonstrating the potential of real‐time strategy in a wider range of applications. Since the data driven method relies on the correlation between plasma plume images and final morphology rather than physical mechanisms, this real‐time imaging strategy can be feasible to the fabrication of other complex micro/nano‐features, such as laser‐induced periodic surface structures (LIPSS), nanospikes, or high‐aspect‐ratio micro‐holes by expanding the training dataset.

To achieve processing optimization for laser micro/nano fabrication, we built an MLP model presented in Figure 5. The model is designed to predict the inner/outer diameter values of coffee‐ring feature structure based on two experimental input parameters: laser power and delay time. The distribution of the input and output testing dataset are shown in Figure 5a,c. The network architecture (Figure 5b) consists of an input layer, three hidden layers (containing 32, 64, and 32 neurons, respectively), and an output layer. The training data is obtained from measured diameters (inner diameters = 2R_i, outer diameters = 2R_o) of the coffee‐ring SEM images, a sample of which is shown in Figure 5d.

FIGURE 5.

Forward MLP prediction of feature structure size. (a) Input data distribution. (b) Forward MLP structure. (c) Output data distribution. (d) Schematic diagram of the fabricated coffee ring structure, the scale bar is 5 µm. (e) Trend of neural network loss function when predicting the inner diameter. (f) Trend of neural network loss function when predicting the outer diameter. (g) Scatter plot of predicted and true inner diameters for the MLP model. (h) Scatter plot of predicted and true outer diameters for the MLP model. (i) Correlation between processing parameters and processing outcomes, OD is outer diameter, ID is inner diameter, and DD is the difference between outer and inner diameters.

The performance of MLP is evaluated by training/validation loss trends and prediction accuracy. Figure 5e,f presents the training and validation loss curves (RMSE) for training inner and outer diameters, respectively. Both loss curves converged into low and stable values, indicating that the model is trained and generalized well without overfitting. The predictive accuracy of the model is demonstrated in the regression plots in Figure 5g (inner diameters) and Figure 5h (outer diameters). These scatter plots show correspondence between the true measured diameters (X‐axis) and predicted diameters (Y‐axis), with data points aligning with the 45‐degree line of perfect agreement. Prediction accuracy is quantitatively confirmed by the coefficients of determination (R²) for the testing dataset, which reached 0.97 for both inner and outer diameter predictions. We use different hyperparameters for the training of forward MLP models to achieve the highest prediction accuracy, other results are presented in Figures S5 and S6. The correlation analysis (Figure 5i) reveals the interaction patterns between laser parameters and processing results, aligning with the physical understanding of the process. Laser power is the dominant factor, exhibiting a strong positive correlation with both inner diameter and outer diameter. Delay time shows a weak correlation with absolute diameters but a negative correlation with the diameter difference.

Building upon the forward model with the same hidden layers architecture, the inverse MLP network is developed to achieve inverse‐designed fabrication by predicting the required processing parameters from specific coffee‐ring sizes. As illustrated in Figure 6a, this inverse model takes the target inner and outer diameters as inputs and outputs the corresponding laser power and delay time. The diameter data used to train the MLP model is obtained from SEM images. Furthermore, the combination of cGAN and MLP models provides a foundation for future closed‐loop control. Real‐time morphological deviations detected by the cGAN can be processed by the MLP to autonomously adjust laser parameters, enabling dynamic error compensation during fabrication. To verify the potential of visual prediction in close‐loop feedback optimization system to achieve inverse‐designed fabrication, we also use the diameter data collected from generated images of cGAN as input to predict corresponding processing parameters based on the inverse model trained on real data.

FIGURE 6.

Inverse designed for the fabrication of a feature structure. (a) Inverse design of a multilayer perceptron to predict processing parameters from processing outcomes, the scale bar is 5 µm. (b) Trend of neural network loss function in inverse design pulse power with real image data. (c) Comparison of inverse‐designed laser power (from real image data) with actual laser power. (d) Comparison of inverse‐designed laser power (from generated image data) with actual laser power. (e) Comparison of inverse‐designed pulse delay time (from real image data) with actual pulse delay time.

The performance of the inverse model is revealed by training/validation loss trends and fit scatter plots. High accuracy in predicting the required laser power using real images is demonstrated. The loss curves for power prediction (Figure 6b) converge to a low and stable RMSE value, confirming the effectiveness of the inverse MLP model. The corresponding scatter plot in Figure 6c also shows data points aligning with the 45‐degree line of perfect agreement, achieving a coefficient of determination (R²) of 0.97 for the testing dataset. As shown in Figure 6d, the inverse design result of laser power based on generated images also achieves a coefficient of determination (R²) of 0.97 at the same time, confirming that the visual prediction results can be used to inverse design processing parameters in real time. In the prediction of delay time, the inverse MLP model exhibits limited capability. Therefore, an additional hidden layer is incorporated to improve prediction performance. The data points are more scattered (Figure 6e) in the prediction of delay time with real image data, displaying a R² of 0.72. The loss curves and inverse design result based on generated images are presented in Figure S7. The lower R² for delay time prediction comes from the physical mechanisms of laser‐material interaction rather than algorithmic limitations. Correlation analysis indicates that delay time has a weaker influence on structure diameters than laser power. In the inverse design task, this weak correlation means that different delay times may produce the same ring diameters, which limits the prediction accuracy for this parameter [35]. To experimentally validate the inverse MLP model, specific target sizes are selected for fabrication. As displayed in Table S2, the processing parameters are inverse designed based on target structural sizes. The resulting coffee‐ring structures are fabricated and measured. The actual dimensions align with the targets, with average relative errors of 4.45% and 3.97% for the inner and outer diameters, respectively. These experimental results confirm the fabrication accuracy of the proposed inverse design model.

3. Conclusions

In summary, we propose a neural networkenabled real‐time plasma imaging strategy, achieving inverse‐designed fabrication of micro/nano structures based on the combination of cGAN and MLP. This strategy is validated by the fabrication of coffee‐ring structures, with a total latency of 1691 milliseconds. Neural networks contain a conditional generative adversarial network (cGAN) for real‐time imaging and a multilayer perceptron (MLP) for inverse‐designed fabrication. The demonstration of generated images with real images qualitatively confirms the performance of cGAN. The convergence of loss curve and the minimum FID score of 44.9 quantitatively assess the training effectiveness of cGAN. Diameter difference heatmaps between real and predicted images demonstrate the predictive performance of the cGAN. Generalization of this strategy is confirmed by predicting surface morphological evolution in sequential single‐pulse processing with different substrate materials. The MLP model established the nonlinear relationships between laser parameters (power and delay time) and feature sizes (inner and outer diameters). Both forward prediction and inverse design of laser power achieved a coefficient of determination (R²) of 0.97. The experiment results of inverse‐designed fabrication align with the targets, with average relative errors of 4.45% and 3.97% for the inner and outer diameters, respectively. These results demonstrate that real‐time imaging can be achieved from a combination of plasma observation and machine learning in ultrafast laser fabrication. Based on the neural networkenabled real‐time imaging strategy, our work provides an alternative for the inverse design of laser parameters and facilitates the development of intelligent laser micro/nano manufacturing.

4. Experimental Section

4.1. Experimental Setup

The substrate material used in experiments is copper (Cu, surface roughness less than 1 nm) and a silicon wafer. Ti: sapphire amplified laser system is used to generate linearly polarized pulses with a duration of 35 fs at a central wavelength of 800 nm and a repetition rate of 1 kHz. The beam is focused onto the sample surface using a 5x objective lens, resulting in a spot diameter (at 1e⁻²) is 9 µm. An intensified charge‐coupled device (ICCD) camera is positioned orthogonally to the beam path to capture the intensity profiles of the plasma plume generated during laser processing. The ICCD is configured with a time width of 2.5 ns and a delay time of 20 ns relative to the incident laser pulse. After processing, the resulting surface morphologies are characterized using a scanning electron microscope (SEM) to obtain ground‐truth images.

4.2. Dataset

A dataset comprising 451 sets of process conditions is collected by varying the laser power from 3 to 13 mW and the dual‐pulse delay time (τ_d) from 30 to 70 ps. For each condition, a pair of images is recorded: the plasma plume intensity profile image and the corresponding SEM image of the final structure. The inner and outer diameters of the elliptical coffee‐ring structures are measured along the major axis from the SEM images. To prevent overfitting and enhance model generalization, the training dataset for the cGAN model is augmented by rotating each image by 90°, 180°, and 270° (Figure S2), resulting in a fourfold increase in dataset size.

4.3. Model Training and Evaluation

All models are implemented using the PyTorch framework and trained on a NVIDIA Tesla V100 GPU supported by the Center for High Performance Computing (Tsinghua University). The original 451‐sample dataset is randomly split into training (90%) and test (10%) sets for the cGAN model. For the MLP model, the split was 80% training, 10% validation, and 10% test. The forward and inverse MLP models are trained for 60 epochs (excluding the delayed prediction) with a batch size of 32. The prediction of delay time is trained for 100 epochs using an MLP model with an added hidden layer. The Adam optimizer is used with a learning rate of 1.2e‐3, and the Root Mean Square Error (RMSE) is employed as the loss function. The choice of hyperparameters enables the model to achieve the best performance, as determined by comparison experiments. The mathematical principles of MLP are presented in the Supporting Information. The cGAN model is trained for 200 epochs with a batch size of 2. The Adam optimizer is configured with a learning rate of 2e‐4 and β₁ = 0.5, β₂ = 0.999. The total loss function is a weighted sum of the GAN loss, feature matching loss, and VGG perceptual loss. The choice of hyperparameters is based on the default values in the original paper, which proposes the pix2pixHD model. Model performance is evaluated using the coefficient of determination (R²) for the MLP regression task and the FID for the image generation task [36]. The FID is calculated using a pre‐trained Inception‐V₃ model to measure the feature‐space distance between the distributions of real and generated images. The calculation formula of FID and R² is given in Supporting Information.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting File 1: adma73601‐sup‐0001‐SuppMat.docx.

Supporting File 2: adma73601‐sup‐0002‐Video1.mp4.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.