Deep learning for non-parameterized MEMS structural design

Machine learning (ML) has revolutionized various fields, and its application to MEMS design is gaining traction. Previous ML-based MEMS design approaches often rely on pre-defined topologies and parameter optimization. This research introduces a novel data-driven non-parameterized design approach, constructing MEMS structures voxel-by-voxel without topological constraints. This approach generates a massive number of design combinations, which poses computational challenges for traditional ML methods. Deep learning (DL), with its ability to handle large datasets and uncover complex patterns, provides a solution. The study focuses on MEMS resonators, crucial components in various applications. Two key properties – resonant frequency and quality (Q) factor – are targeted for prediction. The challenge lies in efficiently finding optimal geometric structures for desired resonant modes and high Q-factors, a task traditionally demanding significant time and resources using numerical analysis. The proposed DL-based method aims to address this challenge by efficiently predicting the physical properties of various resonator designs without relying on extensive FEA simulations.

The paper reviews existing literature on machine learning applications in various fields, highlighting its success in robotics, health informatics, protein engineering, and material discoveries. It also discusses previous work on ML-assisted MEMS design, noting that these often rely on predefined topologies and parameter optimization. The authors position their work as an important alternative using non-parameterized design, enabling the exploration of a significantly larger design space compared to previous methods. The authors highlight the limitations of traditional methods for handling the massive dataset that results from this non-parameterized approach and present deep learning as a superior approach to manage the complexity.

The proposed system consists of a structure generator, FEA simulation, and a DL calculator. The structure generator creates binary images representing resonator structures. FEA, including natural frequency and complex frequency analysis, provides ground truth data (resonant frequency and Q-factor due to anchor loss) for training. The DL model, a customized ResNet, is trained using these labeled samples. The model takes binary images as input and predicts the resonant frequency and Q-factor. Disk-shaped resonators made of polysilicon are used as an example. The resonator geometries are represented as 100x100 binary matrices, where 1 represents a solid element and 0 represents a void. A novel method is employed to generate the structures; an agent moves randomly in a Brownian-like motion, creating a path, which is then folded to produce a symmetrical pattern for the resonator. This agent's trajectory is constrained only by the total area, thereby enabling a highly diverse set of designs. The model architecture utilizes convolutional layers to extract 2D features, max pooling layers for dimensionality reduction, and residual blocks to address the degradation problem in deep networks. FEA involves natural frequency analysis to identify the flexural mode and complex frequency analysis to extract the Q-factor. A method is described to automatically identify the flexural mode using the effective mass tensor from the FEA results, avoiding manual inspection of mode shapes.

The study generated 29,984 unique resonator patterns with varying porosity levels (ratio of void elements). The DL model, after training, accurately predicts the resonant frequency and Q-factor. The model achieves a remarkable speedup compared to FEA: 4.6 × 10³ times faster for frequency prediction (98.8 ± 1.6% accuracy) and 2.6 × 10⁴ times faster for Q-factor prediction (96.8 ± 3.1% accuracy). Simultaneous prediction of both properties saves approximately 96% of computation time. The dataset analysis reveals a typical trade-off between resonant frequency and Q-factor. t-SNE analysis of hidden layer vectors from the DL calculator shows a clear separation of design samples based on frequency and Q-factor values, indicating the model’s ability to capture the underlying relationships between the design and the desired physical properties. The authors demonstrate that even with a complex set of physical interactions, a DL model can be efficiently trained to make precise predictions.

The findings demonstrate the effectiveness of the deep learning approach for accelerating MEMS design. The significant speedup achieved over FEA simulations makes it possible to explore a much larger design space, leading to potentially improved designs. The high accuracy of the predictions suggests that the DL model successfully captures the complex relationship between the resonator geometry and its physical properties. The non-parameterized design approach used in this work provides a significant advantage over traditional methods by enabling the exploration of a wider range of designs, which may not be easily conceived or explored manually. Future work could explore the application of this approach to other types of MEMS devices and the use of more advanced DL architectures.

This paper presents a novel deep learning approach for non-parameterized MEMS structural design. The method significantly accelerates the design process by accurately and rapidly predicting key physical properties, such as resonant frequency and Q-factor, using a deep residual neural network. The approach enables efficient exploration of a vast design space, paving the way for data-driven MEMS design optimization. Future research could focus on extending this method to more complex MEMS structures and exploring other deep learning architectures for further performance enhancements.

The accuracy of the DL model depends on the quality and quantity of the training data. The model was trained and tested on a specific type of MEMS resonator (disk-shaped). The generalizability of the model to other types of resonators or MEMS devices needs further investigation. The Brownian motion based trajectory generation method could be potentially improved by using other algorithms for better exploration of the design space.