  We propose an efficient inverse design approach for multifunctional optical
elements based on adaptive deep diffractive neural networks (a-D$^2$NNs).
Specifically, we introduce a-D$^2$NNs and design two-layer diffractive devices
that can selectively focus incident radiation over two well-separated spectral
bands at desired distances. We investigate focusing efficiencies at two
wavelengths and achieve targeted spectral lineshapes and spatial point-spread
functions (PSFs) with optimal focusing efficiency. In particular, we
demonstrate control of the spectral bandwidths at separate focal positions
beyond the theoretical limit of single-lens devices with the same aperture
size. Finally, we demonstrate devices that produce super-oscillatory focal
spots at desired wavelengths. The proposed method is compatible with current
diffractive optics and doublet metasurface technology for ultracompact
multispectral imaging and lensless microscopy applications.
