update.MuFiMeshGP: update.MuFiMeshGP

In MuFiMeshGP: Multi-Fidelity Emulator for Computer Experiments with Tunable Fidelity Levels

update.MuFiMeshGP

Description

The function updates the current MuFiMeshGP model.

Usage

## S3 method for class 'MuFiMeshGP'
update(object, x, t, y, param.estim = TRUE, init = NULL, ...)

Arguments

object	an object of class MuFiMeshGP.
x	matrix of new input locations.
t	new tunable parameter, a scalar.
y	observation corresponding to input location x and tunable parameter t.
param.estim	if TRUE, the hyper-parameters are estimated by running it through MuFiMeshGP. If FALSE, the hyper-parameters from object are used to update the MuFiMeshGP model fit.
init	See MuFiMeshGP.
...	no other argument.

Details

Updates the MuFiMeshGP model fit with new observations

From the model fitted by MuFiMeshGP or update.MuFiMeshGP the posterior mean and standard deviation are calculated for any input location and fidelity level. For details, see Boutelet and Sung (2025, <arXiv:2503.23158>).

Value

a list which is given the S3 class "MuFiMeshGP"

See Also

MuFiMeshGP for initializing the model.

Examples

# Example code

f <- function(x, t){
  x <- c(x)
  return(exp(-1.4*x)*cos(3.5*pi*x)+sin(40*x)/10*t^2)
}

set.seed(1)
X <- matrix(runif(15,0,1), ncol = 1)
tt <- runif(15,0.5,2)

Y <- f(c(X), tt)

fit.mufimeshgp <- MuFiMeshGP(X, tt, Y)

xx <- matrix(seq(0,1,0.01), ncol = 1)
ftrue <- f(xx, 0)

# predict
pred.mufimeshgp <- predict(fit.mufimeshgp, xx, rep(0,101))

mu <- pred.mufimeshgp$mean
s <- pred.mufimeshgp$sd
lower <- mu + qnorm(0.025)*s
upper <- mu + qnorm(0.975)*s

# plot

oldpar <- par(mfrow = c(1,2))
plot(xx, ftrue, "l", ylim = c(-1,1.3), ylab = "y", xlab = "x")
lines(c(xx), mu, col = "blue")
lines(c(xx), lower, col = "blue", lty = 2)
lines(c(xx), upper, col = "blue", lty = 2)
points(c(X), Y, col = "red")

### RMSE ###
print(sqrt(mean((ftrue - mu))^2))

best <- IMSPE_AL(fit.mufimeshgp, 0.5, 2, function(t) return(1 / t^2))
new.Y <- f(best$x, best$t)
fit.mufimeshgp <- update(fit.mufimeshgp, best$x, best$t, new.Y)

pred.mufimeshgp <- predict(fit.mufimeshgp, xx, rep(0, 101))
mu <- pred.mufimeshgp$mean
s <- pred.mufimeshgp$sd
lower <- mu + qnorm(0.025)*s
upper <- mu + qnorm(0.975)*s

plot(xx, ftrue, "l", ylim = c(-1,1.3), ylab = "y", xlab = "x")
lines(c(xx), mu, col = "blue")
lines(c(xx), lower, col = "blue", lty = 2)
lines(c(xx), upper, col = "blue", lty = 2)
points(c(X), Y, col = "red")
points(c(best$x), new.Y, col = "green")

par(oldpar)

### RMSE ###
print(sqrt(mean((ftrue - mu))^2))

MuFiMeshGP documentation built on Sept. 1, 2025, 5:09 p.m.