PI-Splines: A Structured Spline-Based Architecture for Physics-Informed Learning
Researchers introduce Physics-Informed Splines (PI-Splines), a method that replaces neural networks with tensor-product B-spline expansions for solving differential equations in physics-informed learning. PI-Splines offer compact support, explicit smoothness control, and analytical derivatives, while maintaining the residual-based training approach of Physics-Informed Neural Networks (PINNs). Experiments on benchmark problems demonstrate that PI-Splines are a competitive and stable alternative to neural architectures, especially where structured representations and parameter efficiency are important.
Why it matters: This work offers a structured and interpretable alternative to neural networks for physics-informed machine learning, potentially improving efficiency and stability in scientific computing.
Full story at: arXiv Machine Learning ↗