Mengyang is interested in probabilistic models of multiple time series, images, spatio-temporal data and functional data, with emphasis on scalar computation and theoretical properties. He developed computationally feasible methods and packages for emulating large-scale nonlinear partial differential equations (PDEs), inverse problem, dimension reduction and data fusion, with applications in quantifying uncertain geohazard, climate data and epigenetic studies.  He has research experience in Gaussian random field, Markov random field, latent factor models, stochastic differential equations and filtering algorithms for prediction and uncertainty quantification.