Rearrangement of Single Atoms by Solving Assignment Problems via Convolutional Neural Network
Abstract
:Featured Application
Abstract
1. Introduction
2. Methodology
Model Formulation
3. Convolutional Neural Network Model Formulation
Understand the Data
- Step 1: Dataset preparation: Change the output shape (separate the output digits)
- Step 2: CNN model construction
- Step 3: Model Training
- Training Process
- 1.
- Data Input and Prediction: We input the training data into the CNN model, which processes this data to generate predictions.
- 2.
- Loss Calculation: The model’s predicted output, an array of either or size (depending on grid size), is compared to the actual modified output. The difference between the predicted and actual outputs is measured using the MSE loss function.
- 3.
- Backpropagation and Weight Updates: Through backpropagation, gradients are computed, and the Adam optimizer updates the model weights accordingly.
- 4.
- Training Loop: This process is repeated for a pre-defined number of epochs. To ensure model reliability, the model is saved regularly after every hundred epochs.
- Evaluation Process
- 1.
- Model Evaluation: Post-training, we evaluate the saved models using the test set (20% of datasets). This involves calculating the accuracy of each saved model and counting the number of correct positions predicted in each data instance to ensure that the trained model is not overfitting and can predict well.
- 2.
- Retraining if Necessary: If the evaluated results do not meet our desired goals, we make adjustments to the CNN model parameters or structures and go back to step 3 to retrain again.
4. Results and Discussions
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Problem Size (Target Size) | Number of Datasets | Percentage of Overall Position Accuracy | Percentage of 98% Correct Arrangement | Percentage of 99% Correct Arrangement | Percentage of Defect-Free Arrangement |
---|---|---|---|---|---|
10 × 10 Grid (49 Atoms) | 200,000 | 99.63 | 99.10 | 98.44 | 87.85 |
13 × 13 Grid (81 Atoms) | 600,000 | 98.93 | 95.10 | 89.01 | 68.54 |
21 × 21 Grid (169 Atoms) | 1,000,000 | 97.24 | 87.80 | 59.04 | 4.45 |
Problem Size | Calculation Time per Dataset (Calculation Time 5000 Datasets) | % Time Saving (Time Reduction) | |
---|---|---|---|
Optimal Solution | CNN | ||
10 × 10 Grid | 0.0159 (79.73) s | 0.0031 (15.32) s | 80.50 (5.12 folds) |
13 × 13 Grid | 0.0898 (449.14) s | 0.0048 (24.38) s | 94.65 (18.71 folds) |
21 × 21 Grid | 1.289 (6445.9) s | 0.0061 (30.50) s | 99.53 (211.3 folds) |
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Rattanamongkhonkun, K.; Pongvuthithum, R.; Likasiri, C. Rearrangement of Single Atoms by Solving Assignment Problems via Convolutional Neural Network. Appl. Sci. 2024, 14, 7877. https://doi.org/10.3390/app14177877
Rattanamongkhonkun K, Pongvuthithum R, Likasiri C. Rearrangement of Single Atoms by Solving Assignment Problems via Convolutional Neural Network. Applied Sciences. 2024; 14(17):7877. https://doi.org/10.3390/app14177877
Chicago/Turabian StyleRattanamongkhonkun, Kanya, Radom Pongvuthithum, and Chulin Likasiri. 2024. "Rearrangement of Single Atoms by Solving Assignment Problems via Convolutional Neural Network" Applied Sciences 14, no. 17: 7877. https://doi.org/10.3390/app14177877