  Maxwell equations generally explain the propagation of light through an
arbitrary medium by using wave mechanics. However, scientific evidence since
Newton suggest a discrete interpretation of light more generally explains its
nature. This interpretation lends itself well to the discrete form of computer
simulation. While current simulations attempt to discretize Maxwell equations,
we present an inherently discrete physical model of light propagation that
naturally forms a causal space-time scattering network (STSN). STSN has the
topology of neural networks, inverse design and tomography based on STSN can be
readily implemented in a variety of software and hardware that are optimized
for deep learning. Also, STSN inherently includes the physics of light
propagation, and hence the number of unknown weights in STSN is at a minimum.
We show this property leads to orders of magnitude smaller number of unknown
weights, and a much faster convergence, compared with inverse design methods
using conventional neural networks. In addition, the intrinsic presence of
space-time fabric in STSN allows time-dependent inverse design and tomography.
We show examples of the fast convergence of STSN in predicting time-dependent
index profiles while avoiding approximations typically used.
