Jun Woo Cho

Junwoo Cho, Seungtae Nam, Hyunmo Yang et al.

Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental limitation of training PINNs to solve multi-dimensional PDEs and approximate highly complex solution functions. The number of training points (collocation points) required on these challenging PDEs grows substantially, but it is severely limited due to the expensive computational costs and heavy memory overhead. To overcome this issue, we propose a network architecture and training algorithm for PINNs. The proposed method, separable PINN (SPINN), operates on a per-axis basis to significantly reduce the number of network propagations in multi-dimensional PDEs unlike point-wise processing in conventional PINNs. We also propose using forward-mode automatic differentiation to reduce the computational cost of computing PDE residuals, enabling a large number of collocation points (>10^7) on a single commodity GPU. The experimental results show drastically reduced computational costs (62x in wall-clock time, 1,394x in FLOPs given the same number of collocation points) in multi-dimensional PDEs while achieving better accuracy. Furthermore, we present that SPINN can solve a chaotic (2+1)-d Navier-Stokes equation significantly faster than the best-performing prior method (9 minutes vs 10 hours in a single GPU), maintaining accuracy. Finally, we showcase that SPINN can accurately obtain the solution of a highly nonlinear and multi-dimensional PDE, a (3+1)-d Navier-Stokes equation. For visualized results and code, please see https://jwcho5576.github.io/spinn.github.io/.

Junwoo Cho, Seungtae Nam, Daniel Rho et al.

Neural fields have emerged as a new data representation paradigm and have shown remarkable success in various signal representations. Since they preserve signals in their network parameters, the data transfer by sending and receiving the entire model parameters prevents this emerging technology from being used in many practical scenarios. We propose streamable neural fields, a single model that consists of executable sub-networks of various widths. The proposed architectural and training techniques enable a single network to be streamable over time and reconstruct different qualities and parts of signals. For example, a smaller sub-network produces smooth and low-frequency signals, while a larger sub-network can represent fine details. Experimental results have shown the effectiveness of our method in various domains, such as 2D images, videos, and 3D signed distance functions. Finally, we demonstrate that our proposed method improves training stability, by exploiting parameter sharing.