Compatibility-aware morphology learning for mechanical-acoustic inverse design of functionally graded metamaterials

Functionally graded metamaterials offer a powerful route to spatially tailored properties and multifunctional performance. Their inverse design, however, remains challenging because spatially varying cellular topologies must remain geometrically compatible across neighboring regions, while multiphysics objectives often require time-consuming numerical evaluation. In this work, we introduce a compatibility-aware morphology learning framework for the inverse design of functionally graded metamaterials under expensive multiphysics evaluation. A low-dimensional morphology manifold is learned from cellular structure priors with explicit encoding of boundary compatibility, thereby embedding compatibility directly into the learned representation. This enables continuous geometric transitions among spatially varying unit-cell topologies. Coupled with latent-space optimization and prior-based dataset filtering, the proposed framework substantially reduces design complexity and makes inverse design tractable when target multiphysics are computationally expensive. Mechanical-acoustic inverse design is used as a representative example, in which acoustic response serves as the expensive physics to be simulated while mechanical performance is optimized concurrently. The resultant graded metamaterials are fabricated and experimentally validated through mechanical and acoustic absorption tests. Compared with specimens constructed from a single optimized cellular structure, the inversely designed graded metamaterials exhibit improvements of 58.1% in stiffness and 78.5% in failure loads under bending while maintaining high acoustic absorption.

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