$$\mathcal {C}^k$$-Continuous Spline Approximation with TensorFlow Gradient Descent Optimizers

In this work we present an “out-of-the-box” application of Machine Learning (ML) optimizers for industrial optimization problem. We introduce a piecewise polynomial model (spline) fitting $$\mathcal {C}^k$$ -continuous functions, which can be deployed in cam approximation setting. then use the gradient descent context provided by machine learning framework TensorFlow to optimize parameters with respect quality and -continuity evaluate available optimizers. Our experiments show that problem solution is feasible using tapes AMSGrad SGD best results among Furthermore, novel regularization approach improve convergence. Although remaining discontinuities after are small, eliminate these errors presented algorithm has impact only on affected derivatives local spline segment.