# Polynomial-Spline Neural Networks with Exact Integrals

@article{Actor2021PolynomialSplineNN, title={Polynomial-Spline Neural Networks with Exact Integrals}, author={Jonas A. Actor and Andrew Huang and Nathaniel Trask}, journal={ArXiv}, year={2021}, volume={abs/2110.14055} }

Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address these limitations by formulating a novel neural network architecture incorporating free knot B1-spline basis functions into a polynomial mixture-of-experts model. Effectively, our architecture performs piecewise polynomial approximation on each cell of a…

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