Microscopic structures, such as repeating units of 3D-printed cells, can possess exotic physical properties differing from their underlying material. 

Well-known examples include extreme stiffness at low density, negative refractive index, and negative Poisson ratio.

Metamaterials can be designed for bespoke mechanical, thermodynamic, optical, acoustic and electromagnetic properties.

Thin coatings or structures on material surfaces can be designed to have unusual physical properties.

Just as 3D metamaterials can have exotic properties, e.g. mechanical, optical, acoustic, so can specially engineered 2D metasurfaces.

Well-known examples include anisotropic friction, anti-reflection coatings, and antibacterial properties.

With our knowledge of physics and properties of base materials, we can write and test physics-based simulators for metamaterials.

This is the "forward" simulation problem, and it is well-defined. The "inverse design problem", i.e. calculating the correct structure to fit the required physical properties is, to a traditional physicist, an "ill-posed" problem, since it can have one, zero, or many possible solutions.

"Classically", this is a hard problem. We can leverage AI to solve it.

Machine learning is an approach to AI that tunes the parameters of expressive mathematical models to fit a dataset, rather than to hard-code the logic like a conventional programmer.

Machine learning allows us to use datasets produced by forward simulation of many metamaterials to model the reverse process (inverse design). Generative AI allows us to produce many different suggestions that may meet the requirements.