Structural hierarchy from wavelet zoom and invariant construction

During the past decade there have seen substantial progress being made on materials genome related research. However, coupling mechanisms across multi-scale microstructure and resulting consequences on property and performance of materials remain unsolved problems. Structural hierarchy, which was a concept developed but not quantitatively fulfilled in 1970s, is referred to as microstructure genome here and pinpoints the key enabler for materials genome engineering. Latest progress in deep learning for image recognition and understanding the underlying mathematical mechanisms have revealed the pivotal roles that directional wavelets and invariants play. Hierarchical invariants constructed by a wavelet system can provide an inherent descriptor for microstructure genome.