This paper aims at numerical solution of the partial differential equations (PDEs) with stochastic parameters. We propose a Gaussian-process-based emulator which is capable of choosing the training data adaptively. This model begins with limited training data, trains the Gaussian process emulator, adds the parameters with the highest prediction variance indicator from the parameter pool, along with the corresponding high-fidelity PDE output, into the training data set, until the model achieves a desired accuracy. A 2D parametric diffusion equation is used to test the model. Numerical results demonstrate the efficiency of the model. The accuracy of the model increases rapidly with the growth of training data. Only 40 training data allow us to obtain the desired accuracy.
