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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. 

Abstract Architected materials design across orders of magnitude length scale intrigues exceptional mechanical responses nonexistent in their natural bulk state. However, the so‐termed mechanical metamaterials, when scaling bottom down to the atomistic or microparticle level, remain largely unexplored and conventionally fall out of their coarse‐resolution, ordered‐pattern design space. Here, combining high‐throughput molecular dynamics (MD) simulations and machine learning (ML) strategies, some intriguing atomistic families of disordered mechanical metamaterials are discovered, as fabricated by melt quenching and exemplified herein by lightweight‐yet‐stiff cellular materials featuring a theoretical limit of linear stiffness–density scaling, whose structural disorder—rather than order—is key to reduce the scaling exponent and is simply controlled by the bonding interactions and their directionality that enable flexible tunability experimentally. Importantly, a systematic navigation in the forcefield landscape reveals that, in‐between directional and non‐directional bonding such as covalent and ionic bonds, modest bond directionality is most likely to promotes disordered packing of polyhedral, stretching‐dominated structures responsible for the formation of metamaterials. This work pioneers a bottom‐down atomistic scheme to design mechanical metamaterials formatted disorderly, unlocking a largely untapped field in leveraging structural disorder in devising metamaterials atomistically and, potentially, generic to conventional upscaled designs. 

This paper studies the problem of modeling multi-agent dynamical systems, where agents could interact mutually to influence their behaviors. Recent research predominantly uses geometric graphs to depict these mutual interactions, which are then captured by powerful graph neural networks (GNNs). However, predicting interacting dynamics in challenging scenarios such as out-of-distribution shift and complicated underlying rules remains unsolved. In this paper, we propose a new approach named Prototypical Graph ODE (PGODE) to address the problem. The core of PGODE is to incorporate prototype decomposition from contextual knowledge into a continuous graph ODE framework. Specifically, PGODE employs representation disentanglement and system parameters to extract both object-level and system-level contexts from historical trajectories, which allows us to explicitly model their independent influence and thus enhances the generalization capability under system changes. Then, we integrate these disentangled latent representations into a graph ODE model, which determines a combination of various interacting prototypes for enhanced model expressivity. The entire model is optimized using an end-to-end variational inference framework to maximize the likelihood. Extensive experiments in both in-distribution and out-of-distribution settings validate the superiority of PGODE compared to various baselines.