Improved GEKPLS Function

docs/pages.jl

@@ -15,6 +15,7 @@ pages = ["index.md"
     "Variable Fidelity" => "variablefidelity.md",
     "Gradient Enhanced Kriging" => "gek.md",
     "GEKPLS" => "gekpls.md",
+    "Improved GEKPLS" => "Improvedgekpls.md",
     "MOE" => "moe.md",
     "Parallel Optimization" => "parallel.md",
 ]

docs/src/Improvedgekpls.md

@@ -0,0 +1,55 @@
+# GEKPLS Function
+
+Gradient Enhanced Kriging with Partial Least Squares Method (GEKPLS) is a surrogate modelling technique that brings down computation time and returns improved accuracy for high-dimensional problems. The Julia implementation of GEKPLS is adapted from the Python version by [SMT](https://github.com/SMTorg) which is based on this [paper](https://arxiv.org/pdf/1708.02663.pdf).  
+
+# Modifications for Improved GEKPLS Function:
+
+To enhance the GEKPLS function, sampling method was changed from ```SobolSample()``` to ```HaltonSample()```.
+
+
+```@example gekpls_water_flow
+
+using Surrogates
+using Zygote
+
+function water_flow(x)
+    r_w = x[1]
+    r = x[2]
+    T_u = x[3]
+    H_u = x[4]
+    T_l = x[5]
+    H_l = x[6]
+    L = x[7]
+    K_w = x[8]
+    log_val = log(r/r_w)
+    return (2*pi*T_u*(H_u - H_l))/ ( log_val*(1 + (2*L*T_u/(log_val*r_w^2*K_w)) + T_u/T_l))
+end
+
+n = 1000
+lb = [0.05,100,63070,990,63.1,700,1120,9855]
+ub = [0.15,50000,115600,1110,116,820,1680,12045]
+x = sample(n,lb,ub,HaltonSample())
+grads = gradient.(water_flow, x)
+y = water_flow.(x)
+n_test = 100 
+x_test = sample(n_test,lb,ub,GoldenSample()) 
+y_true = water_flow.(x_test)
+n_comp = 2
+delta_x = 0.0001
+extra_points = 2
+initial_theta = [0.01 for i in 1:n_comp]
+g = GEKPLS(x, y, grads, n_comp, delta_x, lb, ub, extra_points, initial_theta)
+y_pred = g.(x_test)
+rmse = sqrt(sum(((y_pred - y_true).^2)/n_test)) #root mean squared error
+println(rmse) #0.0347
+```
+
+<br>
+<br>
+
+
+
+| **Sampling Method** | **RMSE**                | **Differences**                                                                                                                                                                                                                                                                                     |
+|----------------------|--------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| **Sobol Sampling**               | 0.021472963465423097 | Utilizes digital nets to generate quasi-random numbers, offering low discrepancy points for improved coverage. - Requires careful handling, especially in higher dimensions.                                                                                                                      |
+| **Halton Sampling**               | 0.02144270998045834  | Uses a deterministic sequence based on prime numbers to generate points, allowing for quasi-random, low-discrepancy sampling. - Simpler to implement but may exhibit correlations in some dimensions affecting coverage.