dynemu (version 1.0.0)

dynemu_exact: Predictive posterior computation via exact closed-form expression for one-steap-ahead Gaussian process (GP) emulators

Description

The function computes the predictive posterior distribution (mean and variance) for GP emulators using closed-form expression, given uncertain inputs.

Usage

dynemu_exact(mean, var, dynGP)

Value

A list containing:

• predy: A single-row matrix of predictive mean values, with each column for corresponding state variable.

• predsig2: A single-row matrix of predictive variance values, with each column for corresponding state variable.

Arguments

mean

numeric vector or matrix specifying the mean of uncertain inputs. The number of columns must match the input dimension of `dynGP`.

var

numeric vector or matrix specifying the variance of uncertain inputs. The number of columns must match the input dimension of `dynGP`.

dynGP

list of trained GP emulators fitted by dynemu_GP, each corresponding to a state variable.

Details

Given a trained set of GP emulators `dynGP` fitted using dynemu_GP, this function: 1. Computes the closed-form predictive posterior mean and variance for each state variable. 2. Incorporates input uncertainty by integrating over the input distribution via exact computation.

The computation follows a closed-form approach, leveraging the posterior distributions of Linked GP.

Examples

library(lhs)
### Lotka-Volterra equations ###
LVmod0D <- function(Time, State, Pars) {
  with(as.list(c(State, Pars)), {
    IngestC <- rI * P * C
    GrowthP <- rG * P * (1 - P/K)
    MortC <- rM * C
    
    dP <- GrowthP - IngestC
    dC <- IngestC * AE - MortC
    return(list(c(dP, dC)))
  })
}

### Define parameters ###
pars <- c(rI = 1.5, rG = 1.5, rM = 2, AE = 1, K = 10)

### Define time sequence ###
times <- seq(0, 30, by = 0.01)

### Initial conditions ###
set.seed(1)
d <- 2
n <- 12*d
Design <- maximinLHS(n, d) * 5 # Generate LHS samples in range [0,5]
colnames(Design) <- c("P", "C")

### Fit GP emulators ###
fit.dyn <- dynemu_GP(LVmod0D, times, pars, Design)

### Define uncertain inputs ###
xmean <- c(P = 1, C = 2)
xvar <- c(P = 1e-5, C = 1e-5)

### Compute the next point ###
dynemu_exact(xmean, xvar, fit.dyn)