Meta-Learning for Airflow Simulations with Graph Neural Networks
Wenzhuo Liu Mouadh Yagoubi Marc Schoenauer
The field of numerical simulation is of significant importance for the design
and management of real-world systems, with partial differential equations
(PDEs) being a commonly used mathematical modeling tool. However, solving PDEs
remains still a challenge, as commonly used traditional numerical solvers often
require high computational costs. As a result, data-driven methods leveraging
machine learning (more particularly Deep Learning) algorithms have been
increasingly proposed to learn models that can predict solutions to complex
PDEs, such as those arising in computational fluid dynamics (CFD). However,
these methods are known to suffer from poor generalization performance on
out-of-distribution (OoD) samples, highlighting the need for more efficient
approaches. To this end, we present a meta-learning approach to enhance the
performance of learned models on OoD samples. Specifically, we set the airflow
simulation in CFD over various airfoils as a meta-learning problem, where each
set of examples defined on a single airfoil shape is treated as a separate
task. Through the use of model-agnostic meta-learning (MAML), we learn a
meta-learner capable of adapting to new tasks, i.e., previously unseen airfoil
shapes, using only a small amount of task-specific data. We experimentally
demonstrate the efficiency of the proposed approach for improving the OoD
generalization performance of learned models while maintaining efficiency.