Can I utilize the GPU for Gridsearch in R using lcmm?

Question

I am performing group-based trajectory modeling in R using the lcmm package. This is my code:

fitGbtmql = function(k) {
  start = Sys.time()
  model = do.call(gridsearch, list(m = makeGbtmCallql(k), rep = 5, maxiter = 5, minit = gbtm_modelsql[['1']], cl = 10))
  model$runTime = Sys.time() - start
  return(model)
}

where

makeGbtmCallql(k)

is an hlme function with k clusters. My dataset is very large with around 4.3 million rows. The gridsearch is ofcourse exceptionally time consuming and the 10-core parallel processing doesn't seem to help very much. I can get the cores even higher even to 20 but I doubt it'll make a big difference. If it is any help I believe that the cl argument for parallel processing is based on this code

gridsearch.parallel <- function(m,rep,maxiter,minit,cl=NULL)
{
  if(!is.null(cl)){
    clusterSetRNGStream(cl)
    mc <- match.call()$m
    mc$maxiter <- maxiter
    assign("minit",eval(minit))
    
    clusterCall(cl, function () require(lcmm))
    clusterExport(cl, list("mc", "maxiter", "minit", as.character(as.list(mc[-1])$data)), envir = environment())
    
    cat("Be patient, grid search is running ...\n")
    
    models <- parLapply(cl, 1:rep, function(X)
    {
      mc$B <- substitute(random(minit),parent.frame(n=2))
      return(do.call(as.character(mc[[1]]),as.list(mc[-1])))
    }
    )
    
    llmodels <- sapply(models,function(x){return(x$loglik)})
    
    kmax <- which.max(llmodels)
    mc$B <- models[[kmax]]$best
    mc$maxiter <- NULL
    
    cat("Search completed, performing final estimation\n")
    
    return(do.call(as.character(mc[[1]]),as.list(mc[-1])))
  }
  return(do.call(gridsearch, as.list(match.call()[2:5])))
}

(source: https://github.com/CecileProust-Lima/lcmm/issues/39)

I was wondering if there is a way to run this in another package that usilizes GPU or some other way to speed it up with the CPU (I read some things about hyperthreading, and perhaps turning it off, or something). I am very new in both R and coding and definetely a big noob in machine learning so any advice would be very helpful.

My hardware is: I9-13900k RTX A4000 64GB DDR5