Pipeline ideas

Author: LucasMSpereira

Project.toml

@@ -4,8 +4,10 @@ authors = ["LucasMSpereira"]
 version = "0.1.0"
 
 [deps]
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 ImplicitDifferentiation = "57b37032-215b-411a-8a7c-41a003a55207"
 TopOpt = "53a1e1a5-51bb-58a9-8a02-02056cc81109"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [compat]
 julia = "1"

src/Uncertainty.jl

@@ -1,5 +1,7 @@
 module Uncertainty
 
-# Write your package code here.
-
+struct RandomFunction
+  field
 end
+
+end

test/runtests.jl

@@ -1,6 +1,26 @@
-using Uncertainty
-using Test
+using Uncertainty, Test, ImplicitDifferentiation, Zygote, TopOpt, ChainRulesCore
 
 @testset "Uncertainty.jl" begin
-    # Write your tests here.
-end
+    ## 1) ImplicitDifferentiation.jl -> ensure differentiability
+    zero_gradient(x, y) = 2(y - x) # place-holders from ImplicitDifferentiation.jl docs
+    implicit = ImplicitFunction(???, zero_gradient)
+    x = rand(3)
+    implicit(x)
+    Zygote.jacobian(implicit, x)[1]
+    ## 2) solve optimization -> linear approximation around p0 (MPP)
+    # ???
+    ## linear approximation around p0 and base distribution of parameters -> RandomFunction struct
+    E_p(f(x; p)) = f(x; p = p0) + df(x; p = p0)/dp * mu_p - df(x; p = p0)/dp * p0
+    p ~ MvNormal(mu_p, cov_p)
+    mu(x) = f(x; p = p0(x)) + df(x; p = p0(x))/dp * mu_p - df(x; p = p0(x))/dp * p0
+    cov(x) = (df(x; p = p0)/dp) * cov_p * (df(x; p = p0)/dp)'
+    f(x; p) ~ MvNormal(mu(x), cov(x))
+    rf = RandomFunction(f, MvNormal(zeros(3), I(3)), method = FORM(RIA(g)))
+    ## RandomFunction struct -> mean and cov functions
+    function obj(x)
+        dist = rf(x)
+        mean(dist) + 2 * std(dist)
+    end
+    ## obj(x) to be used in actual application (e.g. TO)
+    # TopOpt.jl code
+end