The kernel is characterized by 𝑥 -𝑥 ′ which is the Euclidean distance between 𝑥 and 𝑥 ′ data points (the input data); 𝑙 is a parameter that signifies the length scale, defining the characteristic length over which variations in the function occur, and α plays a pivotal role governing the balance between large-scale and small-scale fluctuations within the function.