Woven composites are produced by interlacing warp and weft fibers in a pattern or weave style. By changing the pattern or material, the mechanical properties of woven composites can be significantly changed; however, the role of woven composite architecture (pattern, material) on the mechanical properties is not well understood. In this paper, we explore the relationship between woven composite architectures (weave pattern, weave material sequence) and the corresponding modulus through our proposed Physics-Constrained Neural Network (PCNN). Furthermore, we apply statistical learning methods to optimize the woven composite architecture to improve mechanical responses. Our results show that PCNN can effectively predict woven architecture for the desired modulus with much higher accuracy than several baseline models. PCNN can be further combined with feature-based optimization to determine the optimal woven composite architecture at the initial design stage. In addition to relating woven composite architecture to its mechanical responses, our research also provides an in-depth understanding of how architectural features govern mechanical responses. We anticipate our proposed frameworks will primarily facilitate the woven composite analysis and optimization process and be a starting point to introduce Physics knowledge-guided Neural Networks into the complex structural analysis.