update.MuFiMeshGP: update.MuFiMeshGP

Description

The function updates the current MuFiMeshGP model.

Usage

# S3 method for MuFiMeshGP
update(object, x, t, y, param.estim = TRUE, init = NULL, ...)

Value

a list which is given the S3 class "MuFiMeshGP"

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>).

Examples

Run this code

# 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))