$$p$$-Adic Polynomial Regression as Alternative to Neural Network for Approximating $$p$$-Adic Functions of Many Variables

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.