Numerically solving a large parametric nonlinear dynamical system is challenging due to its high complexity and the high computational costs. In recent years, machine-learning-aided non-intrusive surrogate modeling is being actively researched. In this talk, we present two methods in the scope of non-intrusive surrogate modeling. The first method regards extrapolation capability of surrogate models in the time domain. We propose a deep learning framework which generalizes well in thewhole time interval [0, T], when the high-fidelity training data is available only in a training time interval [0, T_0], with T_0 < T. The framework is composed of a convolutional autoencoder (CAE), the kernel dynamic mode decomposition (KDMD) method and a feed-forward neural network (FFNN). The KDMD is employed to evolve the dynamics of the latent space generated by the encoder part of the CAE. The original high-fidelity data set is then augmented with the KDMD-decoder-extrapolated data. We train the CAE along with the FFNN using the augmented data. The trained network yields all-at-once parameter-time sequence prediction at any unseen testing parameters and at any future times t ? [T_0, T], T > T_0. This approach differs from the auto-regressive prediction methods used in existing works. The proposed method is tested on two numerical examples: a FitzHugh-Nagumo model and a model of flow past a cylinder. Numerical results show accurate and fast prediction performance in both the time and the parameter domain. The second method considers active learning for problems with high-dimensional parameter spaces. The training data generation for machine learning (ML) often takes considerable computational or experimental time, and is considered as the most expensive part of ML. 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. 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 CAE and FFNN to construct a surrogate model in MEMS design with many design parameters. A MEMS actuator model with 25 design parameters is tested to show the efficiency of the proposed technique.