Hierarchical inverse design framework for unit-cell CMUTs with attentive gated recurrent and fully connected dense layers

Abstract

Capacitive micromachined ultrasonic transducers (CMUTs) are state-of-the-art devices, generating and detecting ultrasonic waves. They are critical for the next generation of ultrasonic systems due to superior performance, scalability, and integration possibilities relative to conventional piezoelectric transducers. Developing effective inverse design algorithms is required to properly leverage their strengths, streamline design workflows, and push ultrasound technology’s innovative frontiers. In this article, we derive a generalized process to formulate data-centric hierarchical machine-learning (ML)-based inverse design framework. Unit-cell CMUTs are considered as the test case device. In this regard, multidimensional features’ profile database with numbered combinations is generated by finite element method (FEM) for the test case device. Custom feature engineering is formulated to augment the FEM generated database to be compatible with the inverse design mechanics. The proposed inverse design framework consists of hierarchical order of gated recurrent unit (GRU), attention mechanism, and fully connected dense (FCD) layers. Mathematical formulation of the gated-recurrent-attention stack scored through FCD layer stack is derived to model the ML-based regression scheme. Probabilistic search algorithm is formulated to dynamically tune the hyperparameter space concerning the proposed hierarchical architecture. Conventional ML-based regression models such as decision tree (DT), random forest (RF), and linear regression (LR) are considered to analyze the effectiveness of the proposed scheme. Results show that the generalized inverse design framework is immune to the number of the dataset’s available features and the samples of the database, which is due to the designed probabilistic search algorithm’s balanced exploration strategy. Findings show that the proposed scheme achieved the highest goodness-of-fit (r-squared) score of 92% and captures the variation in the database effectively to model the unit-cell CMUTs’ device profile relative to the alternate ML-based regression schemes.