Fit a sum of n gaussians to xy-data and evaluate the best number of n in R

Question

I want to fit a sum of n gaussians to my data of the form: Sum of Gaussians

how would I go around fitting a specified sum of gaussians with the nls() function without specifically writing the individaul parameters like here. I am aware that overfitting becomes a problem, so I want to fit the coefficent of determination for each number of n to graphically determine the best number of n.

To make an reproducilbe example I have this code which resembles my data:

    library(ggplot2)

    # Define a Gaussian function
    gaussian <- function(x, mean, sd, amplitude) {
      amplitude * dnorm(x, mean = mean, sd = sd)
    }

    # Generate x values for plotting
    x <- seq(-10, 10, by = 0.1)

    # Define parameters for 6 Gaussian components
    params <- list(
      list(mean = -2, sd = 1, amplitude = 1),
      list(mean = -1, sd = 0.5, amplitude = 0.8),
      list(mean = 0, sd = 0.3, amplitude = 0.6),
      list(mean = 1, sd = 0.8, amplitude = 0.7),
      list(mean = 2, sd = 0.6, amplitude = 0.5),
      list(mean = 3, sd = 0.4, amplitude = 0.3)
    )

    # Initialize an empty vector to store the sum
    sum_curve <- rep(0, length(x))

    # Sum the Gaussian components
    for (param in params) {
      sum_curve <- sum_curve + gaussian(x, mean = param$mean, sd = param$sd, amplitude = param$amplitude)
    }

    # Create a data frame for plotting
    data <- data.frame(x = x, y = sum_curve)

    # Create the plot for the sum of Gaussian curves
    ggplot(data, aes(x, y)) +
      geom_line() +
      labs(title = "Sum of Gaussian Curves", x = "X", y = "Density") +
      theme_minimal()

To summarize I would kindly ask for help with:

• designing a nls function consisting of a sum of n gaussians
• executing this function for different n (e.g. 1:15) and plotting the results
• plotting the correspondig coefficient of determination against n
• plotting the sum of n gaussians and the individual components.