  We propose Physics-Aware Neural Implicit Solvers (PANIS), a novel,
data-driven framework for learning surrogates for parametrized Partial
Differential Equations (PDEs). It consists of a probabilistic, learning
objective in which weighted residuals are used to probe the PDE and provide a
source of {\em virtual} data i.e. the actual PDE never needs to be solved. This
is combined with a physics-aware implicit solver that consists of a much
coarser, discretized version of the original PDE, which provides the requisite
information bottleneck for high-dimensional problems and enables generalization
in out-of-distribution settings (e.g. different boundary conditions). We
demonstrate its capability in the context of random heterogeneous materials
where the input parameters represent the material microstructure. We extend the
framework to multiscale problems and show that a surrogate can be learned for
the effective (homogenized) solution without ever solving the reference
problem. We further demonstrate how the proposed framework can accommodate and
generalize several existing learning objectives and architectures while
yielding probabilistic surrogates that can quantify predictive uncertainty.
