  Physics-informed neural networks have emerged as an alternative method for
solving partial differential equations. However, for complex problems, the
training of such networks can still require high-fidelity data which can be
expensive to generate. To reduce or even eliminate the dependency on
high-fidelity data, we propose a novel multi-fidelity architecture which is
based on a feature space shared by the low- and high-fidelity solutions. In the
feature space, the projections of the low-fidelity and high-fidelity solutions
are adjacent by constraining their relative distance. The feature space is
represented with an encoder and its mapping to the original solution space is
effected through a decoder. The proposed multi-fidelity approach is validated
on forward and inverse problems for steady and unsteady problems described by
partial differential equations.
