# Recent Research Projects

## Machine Learning EMC

### Machine Learning Applications for Dipole Reconstruction and Near-Field Scanning

### 1. Dipole Source Reconstruction by Convolutional Neural Networks

In the study of RFI problems, equivalent dipole moments are widely used to reconstruct the noise source. The coupled voltage or coupled power can be calculated from the reconstructed dipole sources. Designers can also improve the design to mitigate the coupling based on the equivalent source models.

A machine learning based dipole source reconstruction method using convolutional neural networks (CNN). CNNs are widely used to process 2-D grid data such as images. The picture of the electromagnetic field is fed to the convolutional neural network, and the CNN performs a multi-label classification to determine all types of dominant dipole moments. The CNN also generates a class activation map, which indicates the locations of each type of present dipole moment. With the types and locations of the dipoles known, the magnitude and phase of each dipole can be obtained from LSQ or other optimization methods. With a pre-trained convolutional neural network model, the dipole type and location can be determined in one second and then use optimization algorithms to reconstruct the field pattern. The Center for Electromagnetic Compatibility is continuing to further improve current model and the exploration of using machine learning methodologies to address other possible EMC applications.

## Machine Learning PI

### PDN Modeling and Decap Optimization with Machine Learning

In power distribution networks (PDN) design, there are mainly two challenges nowadays. The first one is efficient modeling for complex PDN systems, while the second one is pre-layout decap optimization. The Center for Electromagnetic Compatibility has been exploring the feasibility of applying machine learning techniques to tackle these problems. The work in this direction is divided into three parts.

### 1. Fast PDN impedance calculation using boundary integration

Modeling PDN and calculating the impedance efficiently for arbitrary board shapes and stackups is important in PDN design. This work employs a boundary element method (BEM) that only needs to discretize the boundary into segments and perform 1D boundary integration to calculate the quasi-static inductances. The inductance matrix between vias for any plane shape can be obtained in seconds through this BEM method. Furthermore, a specialized circuit solver based on the node voltage method is developed to calculate the total impedance from the equivalent circuit for multi-layer PDN structures, so other commercial tools such as Hspice are not needed anymore. The entire algorithm can calculate the PDN impedance much faster than full-wave simulations for multi-layer printed circuit boards (PCB) with arbitrary board shapes and stackups. For example, for a 10-layer printed circuit board (PCB) with 50 decoupling capacitors (decaps), the proposed methodology only requires less than 5 seconds, while full-wave simulations need tens of minutes.

### 2. Fast PDN impedance prediction using deep learning

The superfast computation speed of the proposed method makes it possible and efficient to generate large amounts of PCBs with different board shapes, stackups, IC location, and decap placement for machine learning applications. The first machine learning application is a novel concept of using deep learning for PDN impedance prediction. By adopting the methodology mentioned above, over one million boards with different shapes, stackup, IC location, and decap placement are randomly generated to train a deep neural network (DNN). The trained DNN can predict the impedance accurately for new board configurations that have not been used for training, with a root mean square error (RMSE) of around 1 dB only. The consumed time using the trained DNN is only 0.1 seconds, which is tens of times faster than the BEM method and thousands of times faster than full-wave simulations.

### 3. Decap optimization using deep reinforcement learning

The second machine learning application is using deep reinforcement learning (DRL) for decap optimization. The placement of decoupling capacitors (decaps) is crucial to PDN design but usually challenging due to the enormous search space caused by different locations and decap types. In this work, DRL is used to accelerate the decap optimization process. The DRL model takes board state and partial decap placement as input, and it outputs action probabilities for different decap selection and placement. The algorithm explores different actions according to their probabilities and trains a DNN to make actions with higher rewards more likely to happen. Over 10,000 PCBs with various board shapes, stackups, IC locations, and decap locations are randomly generated to train a DNN to satisfy a target impedance. The trained DNN can predict a high-quality solution for a new PCB within 0.1s. Further, the solution is used as the initial population of a genetic algorithm (GA) that searches for a better solution with fewer decaps. Using the predicted solution by the pre-trained DNN, the search time for the GA to find the optimum solution can be reduced to several minutes. The modeling method and the machine learning techniques proposed in this work are novel and valuable to the efficiency improvement of pre-layout decap optimization and post-layout performance evaluation for PDN systems. The Center for Electromagnetic Compatibility is continuing the innovative exploration of using machine learning methodologies to address PDN problems and other possible EMC applications.

## Machine Learning SI

### Generic Modeling of Differential Striplines Using Machine Learning Based Regression Analysis

In this study, a generic model for a differential stripline is created using machine learning (ML) based regression analysis. A recursive approach of creating various inputs is adapted instead of traditional design of experiments (DoE) approach. This leads to reduction of number of simulations as well as control the data points required for performing simulations. The generic model is developed using considerably smaller number of simulations compared to linear regression models. Additionally, a tabular W-element model of a differential stripline can be used to take the frequency-dependent dielectric loss into effect. This method is easily expanded to a greater number of differential pairs. The frequency range of interest is upto 20 GHz.

A cross-section of a differential stripline used for creating the generic model is shown in the below figure. The inputs to the generic model are geometrical variations like pre-preg and core heightwidth of the conductor, pitch between the differential pair. The height of the dielectric and the thickness of the conductor are kept constant. After the design space of the parameters is defined (see Table I), simulations are performed in Ansys Q2D. Tabulated and frequency dependent RLGC values are extracted from the results. The RLGC values are used as output dataset. A recursive approach was chosen for selecting the number of simulations and levels for each of the input parameters. This means at every step the accuracy of the created generic model is checked. Additional simulations are added to the training dataset until the criteria for accuracy is met. The criteria in this case is the insertion loss to match with 2D simulations within 1 dB. The levels of each input parameter are listed in Table I. While it was observed that a better fit can be obtained using a larger number of simulations, the same effect can be achieved by carefully tuning the number of hidden layers, the input polynomial, the regularization factor, as well as the optimizer. The model is verified with a stripline geometry structure which wasn’t used during the training stage.