Synthetic random heteropolymers (RHPs), composed of a predefined set of monomers, offer a promising strategy for creating protein mimicking materials with tailored biochemical functions. When designed appropriately, RHPs can replicate protein behavior, enabling applications in drug delivery, therapeutic protein stabilization, biosensing, tissue engineering, and medical diagnostics. However, designing RHPs that achieve specific biological functions in a time- and cost-effective manner remains a major challenge. In this talk, I will review this problem and discuss several successful efforts we have made to address it, using statistical, computational, and AI approaches. These include a generalized semi-hidden markov model (GSHMM) and a modified variational autoencoder (VAE) within a semi-supervised framework, designed to capture the structures of critical chemical features as well as individual RHP sequence patterns. These studies highlight the potential of computational approaches to accelerate the rational design of RHPs for a wide range of biological, medical, and healthcare applications.