A method for approximating continuous functions $\mathbb{Z}_{p}^{n}\rightarrow\mathbb{Z}_{p}$ by a linear superposition of continuous functions $\mathbb{Z}_{p}\rightarrow\mathbb{Z}_{p}$ is presented and a polynomial regression model is constructed that allows approximating such functions with any degree of accuracy. A physical interpretation of such a model is given and possible methods for its training are discussed. The proposed model can be considered as a simple alternative to possible $p$-adic models based on neural network architecture.

Triple periodic minimal surfaces (TPMS) have garnered significant interest due to their structural efficiency and controllable geometry, making them suitable for a wide range of applications. This paper investigates the relationships between porosity and persistence entropy with the shape factor of TPMS. We propose conjectures suggesting that these relationships are polynomial in nature, derived through the application of machine learning techniques. This study exemplifies the integration of machine learning methodologies in pure mathematical research. Besides the conjectures, we provide the mathematical models that might have the potential implications for the design and modeling of TPMS structures in various practical applications.

Create a regressor and call it, 'poly_reg'. Assign the regressor to the lm() function as we did in linear regression. The function takes two arguments. The formula and the data, same way we did in linear regression. To transform this from a linear regression to a polynomial regression model, we need to add some polynomial features.

Hello and welcome to this tutorial. We have learnt how to create Single and Multiple linear regression models. Now, let’s learn how to create Polynomial regression Models in R and where we would apply it to solve real life problems. According to Wikipedia, Polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modeled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the correspondent conditional mean of y. In this tutorial we are going to be […]

Create a regressor and call it, 'poly_reg'. Assign the regressor to the lm() function as we did in linear regression. The function takes two arguments. The formula and the data, same way we did in linear regression. To transform this from a linear regression to a polynomial regression model, we need to add some polynomial features.

Now, we get into the more technical part of this article: ML Algorithms. I'll include a TL;DR, although I encourage you to browse through the different algorithms. I'll also include a really helpful AI course video that I personally used to learn and write this article at the very end. Without further wait, let's start going in-depth on the different algorithms used in machine learning. Linear regression is a supervised learning model used for regression that predicts a dependent variable (Y) based on the independent variable(s) (X) by fitting a line linearly.

The linear model is named so because of the linear relationship between the input (independent variable) and the output (dependent variable). Even though we know it's of a high probability that the real-world data shows nonlinearity, people usually keep regarding the linear model as one of the top choices. The reasons for that are mainly two things. First, with acceptable approximation, the linear model is one of the simplest models to interpret. Second, the low complexity of the linear model makes it very unlikely to overfit the data, especially when you have small n (sample size) and large p ( variable number).

The transition from conventional methods of energy production to renewable energy production necessitates better prediction models of the upcoming supply of renewable energy. In wind power production, error in forecasting production is impossible to negate owing to the intermittence of wind. For successful power grid integration, it is crucial to understand the uncertainties that arise in predicting wind power production and use this information to build an accurate and reliable forecast. This can be achieved by observing the fluctuations in wind power production with changes in different parameters such as wind speed, temperature, and wind direction, and deriving functional dependencies for the same. Using optimized machine learning algorithms, it is possible to find obscured patterns in the observations and obtain meaningful data, which can then be used to accurately predict wind power requirements . Utilizing the required data provided by the Gamesa's wind farm at Bableshwar, the paper explores the use of both parametric and the non-parametric models for calculating wind power prediction using power curves. The obtained results are subject to comparison to better understand the accuracy of the utilized models and to determine the most suitable model for predicting wind power production based on the given data set.

In my previous article, we analyzed the COVID-19 data of Turkey and selected the cubic model for predicting the spread of disease. In this article, we will show in detail why we selected the cubic model for prediction and see whether our decision was right or not. When we analyze the regression trend models we should consider overfitting and underfitting situations; underfitting indicates high bias and low variance while overfitting indicates low bias and high variance. The adjusted coefficient of determination is used in the different degrees of polynomial trend regression models comparing. When we examine the above formulas, we can notice the similarity between SSE and bias.

Learn to build a Polynomial Regression model to predict the values for a non-linear dataset. In this article, we will go through the program for building a Polynomial Regression model based on the non-linear data. In the previous examples of Linear Regression, when the data is plotted on the graph, there was a linear relationship between both the dependent and independent variables. Thus, it was more suitable to build a linear model to get accurate predictions. What if the data points had the following non-linearity making the linear model giving an error in predictions due to non-linearity? In this case, we have to build a polynomial relationship which will accurately fit the data points in the given plot.