Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural
  Networks
Woojin Cho Kookjin Lee Donsub Rim Noseong Park
In various engineering and applied science applications, repetitive numerical
simulations of partial differential equations (PDEs) for varying input
parameters are often required (e.g., aircraft shape optimization over many
design parameters) and solvers are required to perform rapid execution. In this
study, we suggest a path that potentially opens up a possibility for
physics-informed neural networks (PINNs), emerging deep-learning-based solvers,
to be considered as one such solver. Although PINNs have pioneered a proper
integration of deep-learning and scientific computing, they require repetitive
time-consuming training of neural networks, which is not suitable for
many-query scenarios. To address this issue, we propose a lightweight low-rank
PINNs containing only hundreds of model parameters and an associated
hypernetwork-based meta-learning algorithm, which allows efficient
approximation of solutions of PDEs for varying ranges of PDE input parameters.
Moreover, we show that the proposed method is effective in overcoming a
challenging issue, known as "failure modes" of PINNs.