新闻 · arXiv cs.LG

Trainable Spline Representations for Physics-Informed Learning

This work introduces Physics-Informed Splines (PI-Splines), a structured spline-based architecture for physics-informed learning. Instead of representing the solution of a differential equation with a neural network, PI-Splines directly parametrize the unknown field through a tensor-product B-spline expansion with trainable control coefficients. This formulation preserves the residual-based training paradigm of Physics-Informed Neural Networks while providing compact support, explicit…