  The application of deep learning toward discovery of data-driven models
requires careful application of inductive biases to obtain a description of
physics which is both accurate and robust. We present here a framework for
discovering continuum models from high fidelity molecular simulation data. Our
approach applies a neural network parameterization of governing physics in
modal space, allowing a characterization of differential operators while
providing structure which may be used to impose biases related to symmetry,
isotropy, and conservation form. We demonstrate the effectiveness of our
framework for a variety of physics, including local and nonlocal diffusion
processes and single and multiphase flows. For the flow physics we demonstrate
this approach leads to a learned operator that generalizes to system
characteristics not included in the training sets, such as variable particle
sizes, densities, and concentration.
