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 smoothness control, analytical derivatives, and a direct geometric interpretation of the trainable parameters. When compatible with the spline representation, boundary conditions can be imposed strongly by f...
| Authors | Giovanni Canali, Nicola Demo, Gianluigi Rozza |
|---|---|
| Primary category | cs.LG |
| Published | 17 July 2026 |
| Last updated at source | 17 July 2026 |
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