Silicon-based anode is one of the promising candidates for the next generation lithium ion batteries (LIBs) to achieve high power/energy density. However, the major drawback limiting the practical application of Si anode is that Si experiences significant volume change during its lithiation/de-lithiation cycles, which induces high stress and causes degradation and pulverization of the anode. This study focuses on the crack initiation performances of Si anode during the de-lithiation process. A multi-physics based finite element (FE) model is built to simulate the electrochemical process and crack generation during de-lithiation. On top of that, a Gaussian Processes (GP) based surrogate model is developed to assist the exploration of the crack initiation performances within the anode design space. It is found that, the thickness of the Si coating layer TSi, the yield strength σFc of Si material, the cohesive strength between Si and substrate σFs, and the curvature of the substrate ρ have large impacts on the cracking behavior of Si. This coupled FE simulation-GP surrogate model framework is also applicable to other types of LIB electrodes.