Determining Thermal Profile and Routing Feasibility

Determining Thermal Profile and Routing Feasibility in 2.5D-Integrated Systems Using Neural Networks Building Regression Models Background: The project focuses on 2.5D-integrated systems, which enable the design of cheaper and more efficient many-core computing systems. We optimize for performance and cost, by determining chiplet location, interposer size, and other features. Chiplet #2 Microbumps Frontside Metal Layer Interposer Substrate Through Silicon Vias [3] Input Layer Output Layer Hidden Layer 2 Hidden Layer 1 Backside Metal Layer Flip Chip Bumps SiP Substrate Preventing Overfitting Collecting data to determine thermal profile and routing feasibility requires Hotspot simulations and linear programming, which are timeconsuming processes. 1 Chiplet #2 [1] Chiplet #3 2 2 1 1 2 Key 1 2 ● ● ● ● ● ● 1.0 0.5 0 5 10 15 20 25 30 35 40 Training Set: 1%, Testing Set: 99%, Epochs = 50 MAE = 0.80°C ≈ 1.0% of Temperature Range. Evaluating Wirelength Regression Model’s Generalization 3.5 Train Error Validation Error 3.0 2.5 2.0 1.5 1.0 0 10 20 30 40 Output Chiplet location. ● Maximum Interposer size. temperature. Frequency. ● Maximum Microbump overhead. wirelength. Network (10 types). Inter-chiplet link design. 140 Conclusions 120 ● Our regression models reduce the time required to determine maximum temperature and wirelength by about 1,500 and 4,000 times, respectively. ● The machine learning models generalize well from the reduced amount of data (1% of the entire dataset) and thus reduce the amount of data needed to be collected by 2 orders of magnitude. 100 80 60 80 60 100 120 140 True Temperature Values (°C) Wirelength Regression Model Performance Preprocessing Data ● Maximum temperature values range approximately between 60°C and 130°C. ● Maximum wirelength values range approximately between 0 mm and 85 mm. Applying Z-Score Normalization to Data ● Mean Absolute Error = 1.80 mm, which is approximately 3% of the wirelength range. ● Runtime to predict max wirelength: ○ Using linear programming: 60 s. ○ Using neural networks: 0.015 s. ○ Speedup: approximately 4,000 times. Predicted Wirelength Values (mm) True Vs Predicted Wirelength Values Output Ranges 70 60 50 40 30 20 10 0 40 20 80 60 True Wirelength Values (mm) Removing Potential Outliers [2] Example of one-hot encoding. True Vs Predicted Temperature Values Predicted Temperature Values (°C) One-hot Encoding Network Type ● Two values in the temperature dataset are potential outliers. ● Removing these from the dataset improves accuracy by decreasing the mean absolute error. ● Mean Absolute Error improves from 0.65°C to 0.54°C. Future Work ● Experiment with parameters in the regression model like number of neurons and the learning rate to determine the optimal network configuration. 80 0 ● Since features have different ranges, we apply z-score normalization to set the same scale for all features and allow easier model convergence. 50 Epochs ● Despite training on only 1% of the entire dataset, the Mean Absolute Error remains within 3% of the output ranges, so both models generalize well to new data. Temperature Regression Model Performance ● Mean Absolute Error (MAE) = 0.65°C , which is approximately 1% of the temperature range. ● Runtime to predict max temperature: ○ Using Hotspot: 20 s. ○ Using neural networks: 0.013 s. ○ Speedup: approximately 1,500 times. (b) Cross-Section View Cross-Section View ● One-hot encoding is a technique to convert categorical variables to numerical input data. ● Convert network type to a one-hot. 1.5 True Vs Predicted Temperature Values Interposer Input 2.0 Training Set: 1%, Testing Set: 99%, Epochs = 50 MAE = 1.96 mm ≈ 3.0% of Wirelength Range. On-Chiplet Channel On-Interposer Channel Chiplet #1 (a) Top Top-Down View View As we train with more epochs, we can plot the training error and validation error for each epoch to see when the two curves begin to diverge, leading to overfitting. The model stops training if the validation score does not improve after 10 epochs, which is another preventative measure against overfitting. Predicted Temperature Values (°C) Chiplet #2 Chiplet #1 [4] Model Evaluation & Optimization Dataset Train Error Validation Error Epochs Validation is used to prevent overfitting, where 20% of the training data is separated to evaluate the model’s metrics after each epoch. Task: Develop a machine learning model to generate accurate predictions for maximum temperature and inter-chiplet wirelength to speed up optimization. Chiplet #3 Evaluating Temperature Regression Model’s Generalization 2.5 0.0 The cross section of a 2.5D system. Interposer ● Collecting data on entire solution space (approximately 1018 examples) is not feasible, so our model must learn to generalize to lots of unseen data based on small training sets. ● Goal: Reduce training set size as long the model maintains satisfactory performance (MAE ≤ 1°C, 2 mm). Mean Absolute Error (mm) Chiplet #1 [1] ● Used TensorFlow to build a regression model that has two densely connected hidden layers with 64 neurons and one output layer. ● The Loss function was set to Mean Squared Error. ● The full dataset sizes are 12,873,388 and 20,496,512 for temperature and wirelength, respectively. ● The full dataset was randomly split into a training set (80%) and a testing set (20%). Generalizing Algorithm Mean Absolute Error (°C) Introduction 130 120 110 100 90 80 70 60 60 70 80 90 100 110 120 130 True Temperature Values (°C)