Since data from real-world phenomenon have noise in it, wouldn't it be useful to add a "noise" term to the recovered formula? The weight (importance) of the noi

Since data from real-world phenomenon have noise in it, wouldn't it be useful to add a "noise" term to the recovered formula? The weight (importance) of the noise term could be adjusted: Low noise would lead to symbologic regression with his structural complexity. High noise would lead to simpler models. In ML, the choice of the noise would be a hyperparameter, determined through minimizing uncertainty on held-out data.