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Electron cyclotron resonance (ECR) plasma etching of silicon carbide is numerically modeled by a feedforward neural network (FNN), which is trained by the Broyden, Fletcher, Goldfarb, and Shanno (BFGS) optimization algorithm and the conventional backpropagation (BP) algorithm. The training samples are obtained from our experimental results, which meet the requirement of Box-Wilson central-composite-designed experimental test design. By using the samples, the BFGS algorithm is compared with the conventional BP algorithm with different hidden neuron numbers, different number of iterations and various learning rates. It is shown that the BFGS algorithm requires less hidden neurons and less iteration to obtain the same training results, and it also provides much smaller cross-validation errors. Therefore, the FNN trained by the BFGS algorithm possesses much better approximation and generalization ability. The silicon carbide ECR process modeling results demonstrate that the FNN trained by the BFGS algorithm are fast, reliable, and accurate.