Silicon-based anode is a promising candidate for next generation lithium-ion batteries (LIBs) with improved energy and power density. However, the practical application of Si anode is hindered by their major reliability issue that Si experiences significant volume change during its lithiation/delithiation cycles, leading to high stress, degradation, and pulverization of the anode. With the development of advanced electrode fabrication technologies, structured Si anodes with delicately designed architectures have been proposed. This study focuses on five triply periodic minimal surface (TPMS) based 3D bi-continuous porous Si anodes, which consist of the nano structured metal scaffolds and conformally coated Si layers and explores their lithiation-induced stresses via numerical methods. The multi-physics based finite element (FE) models are firstly built to simulate the deformation and stress of Si anodes during lithiation processes. Afterwards, the Gaussian Processes (GP) based surrogate model is developed to assist the design optimization of the Si anodes within the design space. It is found that, the inverse FCC and diamond surface-based Si anodes show better performances with the lowest stress concentration. In addition, with the decrease of Si phase volume fraction and increase of scaffold fraction, the stresses can be further reduced.