Second-Order Sensitivity Neural Network Modeling Approach With Applications to Microwave Devices

In this article, a second-order derivative neural network approach is proposed for microwave device modeling to address the situation where not only the input–output relationship but also its high-order derivatives need to be accurately modeled. In this method, the proposed overall model includes the original neural network, the adjoint model, and a second-order derivative model. The new formulation and new sensitivity analysis technique of the second-order derivatives of the neural network are derived. New formulations are deduced for second-order sensitivity modeling of multilayer neural networks with three layers and any number of hidden neurons. To accelerate the training process of the second-order derivative model, a third-order derivative sensitivity analysis is formulated to train the second-order derivative model. The proposed technique can efficiently and accurately represent the input–output relationship with its high-order derivatives. A gallium arsenide (GaAs) metal-semiconductor-field-effect transistor (MESFET) and a measured
$2\,\, {}\times {}50~\mu \text{s}$
gatewidths GaAs Pseudomorphic high-electron-mobility transistor (pHEMT) examples are used to validate the proposed technique.