  Many physics and engineering applications demand Partial Differential
Equations (PDE) property evaluations that are traditionally computed with
resource-intensive high-fidelity numerical solvers. Data-driven surrogate
models provide an efficient alternative but come with a significant cost of
training. Emerging applications would benefit from surrogates with an improved
accuracy-cost tradeoff, while studied at scale. Here we present a
"physics-enhanced deep-surrogate" ("PEDS") approach towards developing fast
surrogate models for complex physical systems, which is described by PDEs.
Specifically, a combination of a low-fidelity, explainable physics simulator
and a neural network generator is proposed, which is trained end-to-end to
globally match the output of an expensive high-fidelity numerical solver.
Experiments on three exemplar testcases, diffusion, reaction-diffusion, and
electromagnetic scattering models, show that a PEDS surrogate can be up to
3$\times$ more accurate than an ensemble of feedforward neural networks with
limited data ($\approx 10^3$ training points), and reduces the training data
need by at least a factor of 100 to achieve a target error of 5%. Experiments
reveal that PEDS provides a general, data-driven strategy to bridge the gap
between a vast array of simplified physical models with corresponding
brute-force numerical solvers modeling complex systems, offering accuracy,
speed, data efficiency, as well as physical insights into the process.
