Large-scale DGP Emulation

Load the packages

library(dgpsi)
library(lhs)

Construct a synthetic simulator

We consider a 2-dimensional synthetic simulator with the following functional form defined over [0, 1] and [0, 1]:

f <- function(x) {
  x1 <- x[,1,drop=F] * 4 -2
  x2 <- x[,2,drop=F] * 4 -2
  y <- 0.5 + ((sin(x1^2-x2^2))^2 - 0.5)/(1 + 0.001*(x1^2+x2^2))^2
  return(y)
 }

We now specify a seed with set_seed() from the package for reproducibility

set_seed(9999)

and generate 3000 training data points:

X <- randomLHS(3000, 2)
Y <- f(X)

Training

We now build and train a large-scale DGP emulator using a Vecchia implementation under our Stochastic Imputation (SI) framework:

m <- dgp(X, Y, vecchia = TRUE)

## Auto-generating a 2-layered DGP structure ... done
## Initializing the DGP emulator ... done
## Training the DGP emulator: 
## Iteration 200: Layer 2: 100%|██████████| 200/200 [02:20<00:00,  1.43it/s]
## Imputing ... done

Validation

After we have the emulator, we can validate it by the Leave-One-Out (LOO) cross validation plot:

plot(m)

## Validating and computing ... done
## Post-processing LOO results ... done
## Plotting ... done

or the Out-Of-Sample (OOS) validation plot over 1000 randomly generated testing locations:

oos_x <- randomLHS(1000, 2)
oos_y <- f(oos_x)
plot(m, oos_x, oos_y)

## Validating and computing ... done
## Post-processing OOS results ... done
## Plotting ... done