physics-informed geometry-aware neural operator
Physics-Informed Geometry-Aware Neural Operator
Numerical solution of partial differential equations (PDEs) has been a very active field of research in the last recent, when in particular Finite Element Method (FEM) was primarily studied. FEM involves discretizing a continuous function space using a discrete mesh and solving high-dimensional a linear system, which can be computationally demanding Dhatt et al. [2012]. This computational cost becomes particularly substantial in tasks requiring repetitive solutions. An example of such tasks is engineering design which necessitates solving parameterized PDEs over a wide range of PDE parameters and domain geometries for design evaluation Almasri et al. [2024]. Recently, machine learning techniques have been introduced to accelerate the process of solving PDEs by learning a neural operator as a mapping from variable PDE parameters and/or domain geometry to the PDE solution Lu et al. [2021]. Once a neural operator model is successfully trained on a dataset, it can generalize to new, unseen parameters and domain geometries. This is done by a single forward pass through the trained neural network, with minimal computational cost.