---
title: >
  Large-scale DGP Emulation
output: rmarkdown::html_vignette
bibliography: references.bib 
description: >
  Large-scale DGP emulation using a Vecchia implementation under the SI.
vignette: >
  %\VignetteIndexEntry{Large-scale DGP Emulation}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  echo = TRUE,
  eval = FALSE
)
```

This vignette gives a demonstration of the package on DGP emulation of large-scale datasets.

## Load the packages

```{r}
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]`:

```{r}
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

```{r}
set_seed(9999)
```

and generate `3000` training data points:

```{r}
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:

```{r}
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:

```{r}
plot(m)
```

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

![](https://raw.githubusercontent.com/mingdeyu/dgpsi-R/master/vignettes/images/vecchia_loo.png){width=100%}

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

```{r}
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
```

![](https://raw.githubusercontent.com/mingdeyu/dgpsi-R/master/vignettes/images/vecchia_oos.png){width=100%}

### Performance tip

The Vecchia implementation in the package leverages the multiple cores available on the machine for multi-thread computation. To optimize performance, it is recommended to experiment with the number of threads using `set_thread_num()`. The current number of threads being used by the package can be checked with `get_thread_num()`.