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Spinodal metamaterials, with architectures inspired by natural phase-separation processes, have presented a significant alternative to periodic and symmetric morphologies when designing mechanical metamaterials with extreme performance. While their elastic mechanical properties have been systematically determined, their large-deformation, nonlinear responses have been challenging to predict and design, in part due to limited data sets and the need for complex nonlinear simulations. This work presents a novel physics-enhanced machine learning (ML) and optimization framework tailored to address the challenges of designing intricate spinodal metamaterials with customized mechanical properties in large-deformation scenarios where computational modeling is restrictive and experimental data is sparse. By utilizing large-deformation experimental data directly, this approach facilitates the inverse design of spinodal structures with precise finite-strain mechanical responses. The framework sheds light on instability-induced pattern formation in spinodal metamaterialsobserved experimentally and in selected nonlinear simulations—leveraging physics-based inductive biases in the form of nonconvex energetic potentials. Altogether, this combined ML, experimental, and computational effort provides a route for efficient and accurate design of complex spinodal metamaterials for large-deformation scenarios where energy absorption and prediction of nonlinear failure mechanisms is essential. 

Metamaterials with functional responses can exhibit varying properties under different conditions (e.g., wave‐based responses or deformation‐induced property variation). This work addresses rapid inverse design of such metamaterials to meet target qualitative functional behaviors, a challenge due to its intractability and nonunique solutions. Unlike data‐intensive and noninterpretable deep‐learning‐based methods, this work proposes the random‐forest‐based interpretable generative inverse design (RIGID), a single‐shot inverse design method for fast generation of metamaterials with on‐demand functional behaviors. RIGID leverages the interpretability of a random forest‐based “design → response” forward model, eliminating the need for a more complex “response → design” inverse model. Based on the likelihood of target satisfaction derived from the trained random forest, one can sample a desired number of design solutions using Markov chain Monte Carlo methods. RIGID is validated on acoustic and optical metamaterial design problems, each with fewer than 250 training samples. Compared to the genetic algorithm‐based design generation approach, RIGID generates satisfactory solutions that cover a broader range of the design space, allowing for better consideration of additional figures of merit beyond target satisfaction. This work offers a new perspective on solving on‐demand inverse design problems, showcasing the potential for incorporating interpretable machine learning into generative design under small data constraints. 

Mechanical metamaterials at the microscale exhibit exotic static properties owing to their en- gineered building blocks, but their dynamic properties have remained significantly less explored. Their design principles can target frequency-dependent properties and resilience upon high-strain-rate deformation, making them versatile materials for applications in lightweight impact resistance, acoustic waveguiding, or vibration damping. However, accessing dynamic properties at small scales has remained a challenge due to low-throughput and destructive characterization, or lack of existing testing protocols. Here we demonstrate a high-throughput non-contact framework that employs MHz-wave propagation signatures within a metamaterial to nondestructively extract dynamic linear properties, omnidirectional elastic information, damping properties, and defect quantification. Using rod-like tessellations of microscopic metamaterials, we report up to 94% direction- and rate-dependent dynamic stiffening at strain rates approaching 10^2 s^{−1}, in addition to damping properties 3 times higher than their constituent materials. We also show that frequency shifts in the vibrational response allow for characterization of invisible defects within the metamaterials, and that selective probing allows for construction of experimental elastic surfaces, previously only possible computationally. Our work provides a route for accelerated data-driven discovery of materials and microdevices for dynamic applications such as protective structures, medical ultrasound, or vibration isolation.