  Machine learning (ML) is emerging as a transformative tool for the design of
architected materials, offering properties that far surpass those achievable
through lab-based trial-and-error methods. However, a major challenge in
current inverse design strategies is their reliance on extensive computational
and/or experimental datasets, which becomes particularly problematic for
designing micro-scale stochastic architected materials that exhibit nonlinear
mechanical behaviors. Here, we introduce a new end-to-end scientific ML
framework, leveraging deep neural operators (DeepONet), to directly learn the
relationship between the complete microstructure and mechanical response of
architected metamaterials from sparse but high-quality in situ experimental
data. The approach facilitates the inverse design of structures tailored to
specific nonlinear mechanical behaviors. Results obtained from spinodal
microstructures, printed using two-photon lithography, reveal that the
prediction error for mechanical responses is within a range of 5 - 10%. Our
work underscores that by employing neural operators with advanced
micro-mechanics experimental techniques, the design of complex
micro-architected materials with desired properties becomes feasible, even in
scenarios constrained by data scarcity. Our work marks a significant
advancement in the field of materials-by-design, potentially heralding a new
era in the discovery and development of next-generation metamaterials with
unparalleled mechanical characteristics derived directly from experimental
insights.
