  For numerical design, the development of efficient and accurate surrogate
models is paramount. They allow us to approximate complex physical phenomena,
thereby reducing the computational burden of direct numerical simulations. We
propose INFINITY, a deep learning model that utilizes implicit neural
representations (INRs) to address this challenge. Our framework encodes
geometric information and physical fields into compact representations and
learns a mapping between them to infer the physical fields. We use an airfoil
design optimization problem as an example task and we evaluate our approach on
the challenging AirfRANS dataset, which closely resembles real-world industrial
use-cases. The experimental results demonstrate that our framework achieves
state-of-the-art performance by accurately inferring physical fields throughout
the volume and surface. Additionally we demonstrate its applicability in
contexts such as design exploration and shape optimization: our model can
correctly predict drag and lift coefficients while adhering to the equations.
