SPINS uses cubic or quintic splines in place of neural networks to minimize a physics-informed residual for ODEs, automatically satisfying boundary conditions and producing smooth, analytically differentiable solutions.
Physics- informed deep b-spline networks for dynamical systems.Transactions on Machine Learning Research, 2026
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A Spline-based Physics-Informed Numerical Scheme: Accurate Smooth Solutions for Differential Equations
SPINS uses cubic or quintic splines in place of neural networks to minimize a physics-informed residual for ODEs, automatically satisfying boundary conditions and producing smooth, analytically differentiable solutions.