Cubic spline as an alternative to methods of machine learning

Approximation of unknown functions in multiple dimensions is an important topic in many areas of industrial engineering, such as nonlinear control. Currently, approaches such as neural networks or fuzzy systems are used to create highly nonlinear surfaces from data. Here we show the capabilities of a very simple classical numerical method such as cubic spline to compete with state of the art machine learning techniques such as Artificial Neural Networks (ANN), Fuzzy Systems (FS), Support Vector Machine (SVM), and Extreme Learning Machines (ELM). Machine learning techniques have many issues such as choosing rules or building a network architecture that can be avoided. Without randomness in the initialization process, there is no need to run the same problem hundreds of times to get a good result. The proposed methods are tested on a variety of problems pertaining to industrial applications against many popular algorithms. Experimental results show that simple cubic splines are indeed competitive in terms of computation time and approximation accuracy when compared with adaptive methods.