$\mathcal{C}^k$-continuous Spline Approximation with TensorFlow Gradient Descent Optimizers
This work addresses an industrial optimization problem for cam design, but it is incremental as it applies existing ML optimizers to a specific domain.
The paper tackles the problem of fitting C^k-continuous splines for cam approximation using TensorFlow gradient descent optimizers, achieving feasible solutions with AMSGrad and SGD showing the best results and introducing a regularization approach to improve SGD convergence.
In this work we present an "out-of-the-box" application of Machine Learning (ML) optimizers for an industrial optimization problem. We introduce a piecewise polynomial model (spline) for fitting of $\mathcal{C}^k$-continuos functions, which can be deployed in a cam approximation setting. We then use the gradient descent optimization context provided by the machine learning framework TensorFlow to optimize the model parameters with respect to approximation quality and $\mathcal{C}^k$-continuity and evaluate available optimizers. Our experiments show that the problem solution is feasible using TensorFlow gradient tapes and that AMSGrad and SGD show the best results among available TensorFlow optimizers. Furthermore, we introduce a novel regularization approach to improve SGD convergence. Although experiments show that remaining discontinuities after optimization are small, we can eliminate these errors using a presented algorithm which has impact only on affected derivatives in the local spline segment.