Advanced Extrapolation Technique for Neural-Based Microwave Modeling and Design

In this paper, an advanced multidimensional extrapolation technique for neural-based microwave modeling and design is proposed to address the modeling challenges in microwave simulation and optimization, such as electromagnetic (EM) optimization and large-signal harmonic balance simulation. A standard neural model is accurate only within the particular range where it is trained by training data, and is unreliable if it is used outside this range. Our proposed method aims to address this issue by extrapolation to provide information and guide the neural network outside the training range. The given training data can be randomly distributed in the input space, and the boundaries of the training region can be arbitrary. The unknown target values of the model outside the training range are formulated as optimization variables and are determined by optimization, such that the first-order continuity of model outputs versus inputs is preserved and the second-order derivatives are minimized everywhere. Formulas for the first-order continuity and the second-order derivatives are derived through the cubic polynomial functions. In this way, the formulation of the proposed method guarantees a good model accuracy inside the training region and makes the model maximally smooth across all directions everywhere outside the training region. Compared with existing extrapolation methods for neural networks, the proposed extrapolation technique makes neural models more robust, resulting in faster convergence in microwave simulation and optimization involving neural model inputs as iterative variables. The validity of the proposed technique is demonstrated using both EM optimization example and nonlinear microwave simulation examples.