From 07c0131068fba8b1393d09834b9e269cd24a65a2 Mon Sep 17 00:00:00 2001 From: Spinachboul Date: Thu, 21 Dec 2023 14:17:04 +0530 Subject: [PATCH 1/5] Improved GEKPLS Function --- docs/pages.jl | 1 + docs/src/Improvedgekpls.md | 56 ++++++++++++++++++++++++++++++++++++++ 2 files changed, 57 insertions(+) create mode 100644 docs/src/Improvedgekpls.md diff --git a/docs/pages.jl b/docs/pages.jl index 24d4d3a7..4d00f6c4 100644 --- a/docs/pages.jl +++ b/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", ] diff --git a/docs/src/Improvedgekpls.md b/docs/src/Improvedgekpls.md new file mode 100644 index 00000000..195c79bf --- /dev/null +++ b/docs/src/Improvedgekpls.md @@ -0,0 +1,56 @@ +# 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 +``` + +
+
+ + + +| **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. | + From 4358bee565c1e98406d8883492fb41170af37dd5 Mon Sep 17 00:00:00 2001 From: MRIDUL JAIN <105979087+Spinachboul@users.noreply.github.com> Date: Thu, 21 Dec 2023 15:26:04 +0530 Subject: [PATCH 2/5] Update Improvedgekpls.md --- docs/src/Improvedgekpls.md | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/docs/src/Improvedgekpls.md b/docs/src/Improvedgekpls.md index 195c79bf..52ac943e 100644 --- a/docs/src/Improvedgekpls.md +++ b/docs/src/Improvedgekpls.md @@ -51,6 +51,5 @@ println(rmse) #0.0347 | **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. | - +| **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. From ef4c12b6d3f720cd216aa070f7d333f5bb93c793 Mon Sep 17 00:00:00 2001 From: MRIDUL JAIN <105979087+Spinachboul@users.noreply.github.com> Date: Thu, 21 Dec 2023 15:26:52 +0530 Subject: [PATCH 3/5] Update Improvedgekpls.md From da68799586b94d9849c6a09c064f46675fb7aca2 Mon Sep 17 00:00:00 2001 From: MRIDUL JAIN <105979087+Spinachboul@users.noreply.github.com> Date: Thu, 21 Dec 2023 15:55:44 +0530 Subject: [PATCH 4/5] Update pages.jl --- docs/pages.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/pages.jl b/docs/pages.jl index 4d00f6c4..455a9702 100644 --- a/docs/pages.jl +++ b/docs/pages.jl @@ -15,7 +15,7 @@ pages = ["index.md" "Variable Fidelity" => "variablefidelity.md", "Gradient Enhanced Kriging" => "gek.md", "GEKPLS" => "gekpls.md", - "Improved GEKPLS" => "Improvedgekpls.md" + "Improved GEKPLS" => "Improvedgekpls.md", "MOE" => "moe.md", "Parallel Optimization" => "parallel.md", ] From dc1d5a82a026ff3f2ca5dd20e6af41ee3cad2f63 Mon Sep 17 00:00:00 2001 From: MRIDUL JAIN <105979087+Spinachboul@users.noreply.github.com> Date: Thu, 28 Dec 2023 16:54:54 +0530 Subject: [PATCH 5/5] Update tensor_prod.md --- docs/src/tensor_prod.md | 19 +++++++++++++++++-- 1 file changed, 17 insertions(+), 2 deletions(-) diff --git a/docs/src/tensor_prod.md b/docs/src/tensor_prod.md index 832603cc..504c7a78 100644 --- a/docs/src/tensor_prod.md +++ b/docs/src/tensor_prod.md @@ -1,6 +1,9 @@ # Tensor product function -The tensor product function is defined as: -``f(x) = \prod_{i=1}^d \cos(a\pi x_i)`` +A tensor product function combines multiple functions or vectors using the tensor product operation. The tensor product is a mathematical operation that takes two vectors and produces another vector space, capturing their joint behavior across multiple dimensions. + +For instance, consider a tensor product function defined as follows: + +```\[ f(x) = ∏ᵢ=₁ᵈ cos(aπxᵢ) \]``` Let's import Surrogates and Plots: ```@example tensor @@ -38,3 +41,15 @@ plot!(xs,f.(xs), label="True function", legend=:top) plot!(xs, loba_1.(xs), label="Lobachevsky", legend=:top) plot!(xs, krig.(xs), label="Kriging", legend=:top) ``` + +## Kriging Plot + +![kriging](https://github.com/Spinachboul/Surrogates.jl/assets/105979087/bf6e2c3d-21e0-46d2-9af4-98ec38e6c462) + +## Lobachevsky Plot + +![lobachevsky](https://github.com/Spinachboul/Surrogates.jl/assets/105979087/743c2f4c-14b5-4c90-89dd-1a57a53a81dd) + +## Combined Plot + +![combined_plot](https://github.com/Spinachboul/Surrogates.jl/assets/105979087/c325ee43-2bb9-4876-9a95-4e902113f2b6)