Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks
This work addresses the need for rapid PDE solvers in engineering applications like aircraft shape optimization, though it is incremental as it builds on existing PINN methods.
The authors tackled the problem of repetitive training in physics-informed neural networks (PINNs) for many-query PDE simulations by proposing lightweight low-rank PINNs with only hundreds of parameters and a hypernetwork-based meta-learning algorithm, achieving efficient approximation across varying input parameters and addressing PINN failure modes.
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.