Merge pull request #359 from vikram-s-narayan/gekpls_with_own_pls

GEKPLS With Custom PLS Based on SKLearn PLS

Author: ChrisRackauckas

Project.toml

@@ -11,6 +11,7 @@ IterativeSolvers = "42fd0dbc-a981-5370-80f2-aaf504508153"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 QuasiMonteCarlo = "8a4e6c94-4038-4cdc-81c3-7e6ffdb2a71b"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [compat]

docs/pages.jl

@@ -14,6 +14,7 @@ pages = ["index.md"
              "Polynomial Chaos" => "polychaos.md",
              "Variable Fidelity" => "variablefidelity.md",
              "Gradient Enhanced Kriging" => "gek.md",
+             "GEKPLS" => "gekpls.md",
          ]
          "User guide" => [
              "Samples" => "samples.md",

docs/src/gekpls.md

@@ -0,0 +1,84 @@
+## GEKPLS Surrogate Tutorial
+
+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).  
+
+The following are the inputs when building a GEKPLS surrogate: 
+
+1. X - The matrix containing the training points
+2. y - The vector containing the training outputs associated with each of the training points
+3. grads - The gradients at each of the input X training points
+4. n_comp - Number of components to retain for the partial least squares regression (PLS)
+5. delta_x -  The step size to use for the first order Taylor approximation
+6. xlimits - The lower and upper bounds for the training points
+7. extra_points - The number of additional points to use for the PLS 
+8. theta - The hyperparameter to use for the correlation model
+
+The following example illustrates how to use GEKPLS:
+
+```@example gekpls_water_flow
+
+using Surrogates
+using Zygote
+
+function vector_of_tuples_to_matrix(v)
+    #helper function to convert training data generated by surrogate sampling into a matrix suitable for GEKPLS
+    num_rows = length(v)
+    num_cols = length(first(v))
+    K = zeros(num_rows, num_cols)
+    for row in 1:num_rows
+        for col in 1:num_cols
+            K[row, col]=v[row][col]
+        end
+    end
+    return K
+end
+
+function vector_of_tuples_to_matrix2(v)
+    #helper function to convert gradients into matrix form
+    num_rows = length(v)
+    num_cols = length(first(first(v)))
+    K = zeros(num_rows, num_cols)
+    for row in 1:num_rows
+        for col in 1:num_cols
+            K[row, col] = v[row][1][col]
+        end
+    end
+    return K
+end
+
+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
+d = 8
+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,SobolSample())
+X = vector_of_tuples_to_matrix(x)
+grads = vector_of_tuples_to_matrix2(gradient.(water_flow, x))
+y = reshape(water_flow.(x),(size(x,1),1))
+xlimits = hcat(lb, ub)
+n_test = 100 
+x_test = sample(n_test,lb,ub,GoldenSample()) 
+X_test = vector_of_tuples_to_matrix(x_test) 
+y_true = water_flow.(x_test)
+n_comp = 2
+delta_x = 0.0001
+extra_points = 2
+initial_theta = 0.01
+g = GEKPLS(X, y, grads, n_comp, delta_x, xlimits, 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)
+```
+