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Abstract Multifunctional metamaterials (MMM) bear promise as next‐generation material platforms supporting miniaturization and customization. Despite many proof‐of‐concept demonstrations and the proliferation of deep learning assisted design, grand challenges of inverse design for MMM, especially those involving heterogeneous fields possibly subject to either mutual meta‐atom coupling or long‐range interactions, remain largely under‐explored. To this end, a data‐driven design framework is presented, which streamlines the inverse design of MMMs involving heterogeneous fields. A core enabler is implicit Fourier neural operator (IFNO), which predicts heterogeneous fields distributed across a metamaterial array, thus in general at odds with homogenization assumptions. Additionally, a standard formulation of inverse problem covering a broad class of MMMs is presented, together with gradient‐based multitask concurrent optimization identifying a set of Pareto‐optimal architecture‐stimulus (A‐S) pairs. Fourier multiclass blending is proposed to synthesize inter‐class meta‐atoms anchored on a set of geometric motifs, while enjoying training‐free dimension reduction and built‐it reconstruction. Interlocking the three pillars, the framework is validated for light‐by‐light programmable nanoantenna, whose design involves vast space jointly spanned by quasi‐freeform supercells, maneuverable incident phase distributions, and conflicting figure‐of‐merits (FoM) involving on‐demand localization patterns. Accommodating all the challenges, the framework can propel future advancements of MMM. 

Abstract Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach. In this work, we propose a learning framework to extract a peridynamics model as a mesoscale continuum surrogate from MD simulated material fracture data sets. Firstly, we develop a novel coarse-graining method, to automatically handle the material fracture and its corresponding discontinuities in the MD displacement data sets. Inspired by the weighted essentially non-oscillatory (WENO) scheme, the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil, then reconstruct the coarse-grained material displacement field as the piecewise smooth solutions containing discontinuities. Then, based on the coarse-grained MD data, a two-phase optimization-based learning approach is proposed to infer the optimal peridynamics model with damage criterion. In the first phase, we identify the optimal nonlocal kernel function from the data sets without material damage to capture the material stiffness properties. Then, in the second phase, the material damage criterion is learnt as a smoothed step function from the data with fractures. As a result, a peridynamics surrogate is obtained. As a continuum model, our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training, and hence allows for substantial reductions in computational cost compared with MD. We illustrate the efficacy of the proposed approach with several numerical tests for the dynamic crack propagation problem in a single-layer graphene. Our tests show that the proposed data-driven model is robust and generalizable, in the sense that it is capable of modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training. 

Nonlocal operators with integral kernels have become a popular tool for designing solution maps between function spaces, due to their efficiency in representing long-range dependence and the attractive feature of being resolution-invariant. In this work, we provide a rigorous identifiability analysis and convergence study for learning kernels in nonlocal operators. It is found that kernel estimation is an ill-posed or even ill-defined inverse problem, leading to divergent estimators in the presence of modeling errors or measurement noises. To resolve this issue, we propose a nonparametric regression algorithm with a novel data-adaptive RKHS Tikhonov regularization method based on the function space of identifiability. The method yields a noisy-robust convergent estimator of the kernel as the data resolution refines, on both synthetic and real-world datasets. In particular, the method successfully learns a homogenized model for stress wave propagation in a heterogeneous solid, revealing the unknown governing laws from real-world data at the microscale. Our regularization method outperforms baseline methods in robustness, generalizability, and accuracy.