Reproduce “Separable Physics-Informed Neural Networks” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Junwoo Cho, Seungtae Nam, Hyunmo Yang, Seok-Bae Yun, Youngjoon Hong, Eunbyung Park
Separable Physics-Informed Neural Networks (SPINN) introduces an architectural and training methodology to significantly improve the scalability and computational efficiency of PINNs for multi-dimensional partial differential equations. SPINN achieves up to a 62x reduction in training time and 1394x fewer FLOPs, enabling accurate solutions for high-dimensional, complex PDEs like 4D Navier-Stokes on commodity hardware.
Key insights
- Decomposing a multi-dimensional function into a sum of products of 1D functions significantly reduces the computational complexity of derivative calculations required for PINNs.
- Forward-mode AD is uniquely efficient for computing derivatives when the input dimension is smaller than the output dimension, a property exploited by the 1D body-networks in SPINN.
- The combination of a separable network, factorizable coordinates, and targeted forward-mode AD effectively mitigates the curse of dimensionality, allowing PINNs to scale to unprecedented numbers of collocation points.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.