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Designing complex, dynamic yet multi-functional materials and devices is challenging because the design spaces for these materials have numerous interdependent and often conflicting constraints. Taking inspiration from advances in artificial intelligence and their applications in material discovery, we propose a computational method for designing metamorphic DNA-co-polymerized hydrogel structures. The method consists of a coarse-grained simulation and a deep learning-guided optimization system for exploring the immense design space of these structures. Here, we develop a simple numeric simulation of DNA-co-polymerized hydrogel shape change and seek to find designs for structured hydrogels that can fold into the shapes of different Arabic numerals in different actuation states. We train a convolutional neural network to classify and score the geometric outputs of the coarse-grained simulation to provide autonomous feedback for design optimization. We then construct a genetic algorithm that generates and selects large batches of material designs that compete with one another to evolve and converge on optimal objective-matching designs. We show that we are able to explore the large design space and learn important parameters and traits. We identify vital relationships between the material scale size and the range of shape change that can be achieved by individual domains and we elucidate trade-offs between different design parameters. Finally, we discover material designs capable of transforming into multiple different digits in different actuation states.