Transfer learning-assisted inverse modeling in nanophotonics based on
  mixture density networks
Liang Cheng Prashant Singh Francesco Ferranti
The simulation of nanophotonic structures relies on electromagnetic solvers,
which play a crucial role in understanding their behavior. However, these
solvers often come with a significant computational cost, making their
application in design tasks, such as optimization, impractical. To address this
challenge, machine learning techniques have been explored for accurate and
efficient modeling and design of photonic devices. Deep neural networks, in
particular, have gained considerable attention in this field. They can be used
to create both forward and inverse models. An inverse modeling approach avoids
the need for coupling a forward model with an optimizer and directly performs
the prediction of the optimal design parameters values.
  In this paper, we propose an inverse modeling method for nanophotonic
structures, based on a mixture density network model enhanced by transfer
learning. Mixture density networks can predict multiple possible solutions at a
time including their respective importance as Gaussian distributions. However,
multiple challenges exist for mixture density network models. An important
challenge is that an upper bound on the number of possible simultaneous
solutions needs to be specified in advance. Also, another challenge is that the
model parameters must be jointly optimized, which can result computationally
expensive. Moreover, optimizing all parameters simultaneously can be
numerically unstable and can lead to degenerate predictions. The proposed
approach allows overcoming these limitations using transfer learning-based
techniques, while preserving a high accuracy in the prediction capability of
the design solutions given an optical response as an input. A dimensionality
reduction step is also explored. Numerical results validate the proposed
method.