Continuous-time dynamics models, e.g., neural ordinary differential equations, enable accurate modeling of underlying dynamics in time-series data. However, employing neural networks for parameterizing dynamics makes it challenging for humans to identify dependence structures, especially in the presence of delayed effects. In consequence, these models are not an attractive option when capturing dependence carries more importance than accurate modeling, e.g., in tsunami forecasting.

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.