Reproduce “SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs” on OpenResearch

About this paper

Amuthan A. Ramabathiran, Prabhu Ramachandran

A novel neural network architecture, SPINN (Sparse, Physics-based, and partially Interpretable Neural Networks), is introduced for solving ordinary and partial differential equations by reinterpreting meshless approximations as sparse neural networks. The model achieves accurate and adaptive solutions for challenging problems, including highly oscillatory ODEs and shock-forming PDEs, often with greater efficiency than dense Physics-Informed Neural Networks.

Key insights

• A direct connection can be established between certain meshless approximations and sparse DNN architectures, enabling the construction of neural networks for PDEs with inherent interpretability.
• Allowing node positions and kernel widths to be trainable parameters within the SPINN architecture facilitates implicit mesh adaptivity, enabling the network to dynamically refine its resolution in critical solution regions.
• SPINN offers a seamless bridge between dense neural network methods and traditional mesh-free numerical methods, opening avenues for developing hybrid algorithms that leverage the strengths of both paradigms.

Summary by alphaXiv.