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Advances in data-driven design and additive manufacturing have substantially accelerated the development of truss metamaterials—three-dimensional truss networks—offering exceptional mechanical properties at a fraction of the weight of conventional solids. While existing design approaches can generate metamaterials with target linear properties, such as elasticity, they struggle to capture complex nonlinear behaviours and to incorporate geometric and manufacturing constraints—including defects—crucial for engineering applications. Here we present GraphMetaMat, an autoregressive graph-based framework capable of designing three-dimensional truss metamaterials with programmable nonlinear responses, originating from hard-to-capture physics such as buckling, frictional contact and wave propagation, along with arbitrary geometric constraints and defect tolerance. Integrating graph neural networks, physics biases, imitation learning, reinforcement learning and tree search, we show that GraphMetaMat can target stress–strain curves across four orders of magnitude and vibration transmission responses with varying attenuation gaps, unattainable by previous methods. We further demonstrate the use of GraphMetaMat for the inverse design of novel material topologies with tailorable high-energy absorption and vibration damping that outperform existing polymeric foams and phononic crystals, potentially suitable for protective equipment and electric vehicles. This work sets the stage for the automatic design of manufacturable, defect-tolerant materials with on-demand functionalities. 

Abstract Designing and printing metamaterials with customizable architectures enables the realization of unprecedented mechanical behaviors that transcend those of their constituent materials. These behaviors are recorded in the form of response curves, with stress-strain curves describing their quasi-static footprint. However, existing inverse design approaches are yet matured to capture the full desired behaviors due to challenges stemmed from multiple design objectives, nonlinear behavior, and process-dependent manufacturing errors. Here, we report a rapid inverse design methodology, leveraging generative machine learning and desktop additive manufacturing, which enables the creation of nearly all possible uniaxial compressive stress‒strain curve cases while accounting for process-dependent errors from printing. Results show that mechanical behavior with full tailorability can be achieved with nearly 90% fidelity between target and experimentally measured results. Our approach represents a starting point to inverse design materials that meet prescribed yet complex behaviors and potentially bypasses iterative design-manufacturing cycles. 

Printed low-density materials form microrobots capable of high-speed motion, force output, and self-sensing feedback.