Scientific machine learning (SciML) is widely used in many research areas to fast predict many phenomena, such as material properties, device performances, or fluid dynamics that change not only with time/frequency but also with physical, geometrical, or material parameters. Usually, SciML needs a large amount of data for training a neural network (NN). The training data generation often takes considerable computational or experimental time, and is considered as the most expensive part of SciML. This becomes especially time-consuming for problems with high-dimensional parameter spaces, where the training data increases exponentially with the number of samples in each parameter dimension. How to properly choose or generate the training data as less as possible, without weakening the ability of the NN generalization, has not yet been intensively studied in the literature. In this work, we propose an active learning technique for generating the training data only on demand, so that the finally trained NN requires much less training data and still achieves good accuracy, as compared to NN training without active learning. This technique is combined with a convolutional autoencoder (CAE) and a feed-forward NN (FFNN)~\cite{morNikKP22} to construct a surrogate model in MEMS design with many design parameters. Once finished training, FFNN combined with the decoder is used to do fast online prediction at any testing parameter samples. Starting with a small training data set generated by a finite element method (FEM) simulation tool, the proposed active learning method iteratively expands the small data set until the prediction error over a large testing parameter sample set, is small enough. The prediction error is estimated using two cheaply computable criteria without generating any new testing data corresponding to the testing parameter sample set. The FEM simulation tool is only informed with the poor predictions indicated by large prediction errors to generate new training data. A MEMS actuator model with 25 design parameters is tested to show the efficiency of the proposed technique. Active learning finally selected 532 training data, the trained NN has acceptable average prediction error of 0.06 over all the testing parameter samples. Without active learning, the same NN trained with 600 training data, leads to a much larger error of 0.18. This indicates that active learning guides SciML to use less training data but to achieve even better accuracy.