Silicon-based anodes are one of the promising candidates for the next generation high-power/energy density lithium ion batteries (LIBs). However, a major drawback limiting the practical application of the Si anode is that Si experiences a significant volume change during lithiation/delithiation, which induces high stresses causing degradation and pulverization of the anode. This study focuses on crack initiation within a Si anode during the delithiation process. A multi-physics-based finite element (FE) model is built to simulate the electrochemical process and crack generation during delithiation. On top of that, a Gaussian process (GP)-based surrogate model is developed to assist the exploration of the crack patterns within the anode design space. It is found that the thickness of the Si coating layer, TSi, the yield strength of the Si material, σFc, the cohesive strength between Si and the 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 and provides fundamental insights as building blocks to investigate more complex internal geometries.