Surface topographies of materials considerably impact cellular behavior as they have been shown to affect cell growth, provide cell guidance, and even induce cell differentiation. Consequently, for successful application in tissue engineering, the contact interface of biomaterials needs to be optimized to induce the required cell behavior. However, a rational design of biomaterial surfaces is severely hampered because knowledge is lacking on the underlying biological mechanisms. Therefore, we previously developed a high-throughput screening device (TopoChip) that measures cell responses to large libraries of parameterized topographical material surfaces. Here, we introduce a computational analysis of high-throughput materiome data to capture the relationship between the surface topographies of materials and cellular morphology. We apply robust statistical techniques to find surface topographies that best promote a certain specified cellular response. By augmenting surface screening with data-driven modeling, we determine which properties of the surface topographies influence the morphological properties of the cells. With this information, we build models that predict the cellular response to surface topographies that have not yet been measured. We analyze cellular morphology on 2176 surfaces, and find that the surface topography significantly affects various cellular properties, including the roundness and size of the nucleus, as well as the perimeter and orientation of the cells. Our learned models capture and accurately predict these relationships and reveal a spectrum of topographies that induce various levels of cellular morphologies. Taken together, this novel approach of high-throughput screening of materials and subsequent analysis opens up possibilities for a rational design of biomaterial surfaces.