Mesoscopic simulations and multi-dimensional optimization of natural convection in porous media are investigated. The challenges of this problem exist in three aspects. The first one is how to generate porous structures with various microscopic geometries. The second is how to simulate the fluid flow, heat and mass diffusion, and their convection with buoyancy forces in multiple length scales and time scales. And the third is how to fill the gap between the sparse scattered physics-based small number of data set and the needs of big data set number for prediction. A Controllable Structure Generation Scheme (CSGS) based on discrete Gaussian quadrature space and velocity is developed to generate multiple-phase structures of both random isotropic homogeneous type and shape-constrained anisotropic heterogeneous types. Non-Dimensional Lattice Boltzmann (NDLBM) is developed to simulate the fluid flow, conjugate heat and mass transfer in mesoscopic scales. The porosity-based bounce back scheme is used to perform the non-slip conditions for solid-fluid interferes in arbitrary structures. The parallel scheme of NDLBM (P-NDLBM) is used to speed up the computation of transient fluid flow, heat and mass transfer with larger grid numbers and simulation times. An artificial intelligence (AI) based optimization framework is developed to integrate prediction with Artificial Neural Networks (ANNs), optimization with the weighted objective function, and physics-based P-NDLBM simulation. Validations have been done by comparison with previous experimental and numerical studies. Simulations are performed based on wide ranges of dimensionless mesoscopic governing parameters obtained by the scale analysis. Optimal and off-optimal cases are compared with the underlying physics results to guide coupled fluid flow, heat and mass transfer in porous media with different structures.