Exploring Machine Learning Techniques for Predictive Analytics in Computational Mathematics

The machine learning (ML) called predictive analytics has become a useful tool in computer mathematics. It lets you make models that can predict what will happen in the future based on data from the past. This paper looks at several machine learning (ML) methods used in predictive analytics within the field of computational mathematics. It focuses on how they work, what they can be used for, and how well they work. We look at regression analysis, neural networks, decision trees, support vector machines (SVM), and ensemble methods in depth, looking at both their theoretical bases and how they are used in real life. It is possible to understand how factors are related using regression analysis, which includes both linear and polynomial regressions. However, because it is so simple, it may not be able to be used for complicated, non-linear situations. Because they are based on biological systems, neural networks are very good at making predictions, especially when dealing with big datasets with lots of complex patterns. But their training process uses a lot of computers and a lot of skill to keep it from overfitting. Decision trees work well for classification and regression tasks because they are simple and easy to understand, but they can become unstable when small changes happen in the data. Because they are based on strong theory, support vector machines work best in spaces with a lot of dimensions and are especially good at solving classification problems. Some methods, like random forests and gradient boosting, use more than one model to make predictions more accurate and reliable. However, they can use a lot of resources and be hard to tune. This paper gives a full picture of what's going on in predictive analytics for computational mathematics by comparing the pros and cons of each method. The new information is meant to help academics and practitioners choose the right machine learning methods for their specific predictive modeling needs. This will eventually help the field of computational mathematics by making predictive analytics more accurate and efficient.