Silicon-based lithium ion battery anodes are attracting considerable attention due to their high theoretical capacity. However, the significant volume change of silicon during lithiation/de-lithiation cycles restricts its application. A novel bi-continuous Si anode, designed to mitigate the effect of cycling-induced volume changes, is investigated in this study. The effects of the design parameters and the operating conditions of the anode are explored via multi-physics simulation model. It is found that, with the novel anode structure, battery charging C rate has little impact on the mechanical properties. However, the anode structural design parameters would largely influence the stress distribution on the anode. Thus, a Gaussian Processes (GP) based surrogate model is developed to assist the design optimization of the Si anode, while using the simulated results from a multiphysics simulation model as training data. An optimized Si anode design can then be extracted efficiently based upon the developed surrogate model.