  Nowadays, Computational Fluid Dynamics (CFD) is a fundamental tool for
industrial design. However, the computational cost of doing such simulations is
expensive and can be detrimental for real-world use cases where many
simulations are necessary, such as the task of shape optimization. Recently,
Deep Learning (DL) has achieved a significant leap in a wide spectrum of
applications and became a good candidate for physical systems, opening
perspectives to CFD. To circumvent the computational bottleneck of CFD, DL
models have been used to learn on Euclidean data, and more recently, on
non-Euclidean data such as unstuctured grids and manifolds, allowing much
faster and more efficient (memory, hardware) surrogate models. Nevertheless, DL
presents the intrinsic limitation of extrapolating (generalizing) out of
training data distribution (design space). In this study, we present a novel
work to increase the generalization capabilities of Deep Learning. To do so, we
incorporate the physical gradients (derivatives of the outputs w.r.t. the
inputs) to the DL models. Our strategy has shown good results towards a better
generalization of DL networks and our methodological/ theoretical study is
corroborated with empirical validation, including an ablation study.

Fluid Dynamics;Machine Learning;Numerical Analysis;Numerical Analysis