  Multifidelity simulation methodologies are often used in an attempt to
judiciously combine low-fidelity and high-fidelity simulation results in an
accuracy-increasing, cost-saving way. Candidates for this approach are
simulation methodologies for which there are fidelity differences connected
with significant computational cost differences. Physics-informed Neural
Networks (PINNs) are candidates for these types of approaches due to the
significant difference in training times required when different fidelities
(expressed in terms of architecture width and depth as well as optimization
criteria) are employed. In this paper, we propose a particular multifidelity
approach applied to PINNs that exploits low-rank structure. We demonstrate that
width, depth, and optimization criteria can be used as parameters related to
model fidelity, and show numerical justification of cost differences in
training due to fidelity parameter choices. We test our multifidelity scheme on
various canonical forward PDE models that have been presented in the emerging
PINNs literature.
