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sdwfrost/surrogates-example.ipynb

Created March 4, 2021 14:48
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mogp example in Surrogates.jl
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surrogates-example.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using OrdinaryDiffEq\n",
"using DiffEqCallbacks\n",
"using Surrogates\n",
"using Plots"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"f (generic function with 1 method)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function f(du,u,p,t)\n",
" c = p[1]\n",
" vx,vy,x,y = u\n",
" du[1] = -c*vx*sqrt(vx^2 + vy^2)\n",
" du[2] = -9.8 - c*vy*sqrt(vx^2 + vy^2)\n",
" du[3] = vx\n",
" du[4] = vy\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"function event(u,t,integrator) # Event when event_f(u,t) == 0\n",
" u[4]\n",
"end;"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"affect!(integrator) = terminate!(integrator);"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"cb = DiffEqCallbacks.ContinuousCallback(event,affect!);"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"p = [0.01]\n",
"u0 = [100.0/sqrt(2.0), 100.0/sqrt(2.0),0.0,2.0]\n",
"tspan = (0.0,100.0)\n",
"prob = ODEProblem(f,u0,tspan,p,jac=true)\n",
"sol = solve(prob,Tsit5(),callback=cb);"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
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" \"/>\n",
"</svg>\n"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(sol[3,:],sol[4,:],\n",
" xlabel=\"Horizontal distance (m)\",\n",
" ylabel=\"Vertical distance (m)\",\n",
" title=\"Projectile hits at \" * string(sol[end][3]),\n",
" legend=false)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"function simulator(z,prob=prob)\n",
" p = [10.0^z[1]]\n",
" u0 = [z[2]/sqrt(2.0),z[2]/sqrt(2.0),0.0,2.0]\n",
" tspan = (0.0,100.0)\n",
" prob = remake(prob;u0=u0,tspan=tspan,p=p)#ODEProblem(sys,u0,tspan,p,jac=false)\n",
" sol = solve(prob,Tsit5(),callback=cb)\n",
" return sol[end][3]\n",
"end;"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"lower_bound = [-5.0,0.0]\n",
"upper_bound = [0.0,1000.0]\n",
"n_simulations = 50\n",
"simulation_points = sample(n_simulations, lower_bound, upper_bound, LatinHypercubeSample());"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 7.287173 seconds (13.84 M allocations: 1.047 GiB, 4.40% gc time)\n"
]
}
],
"source": [
"@time simulation_output = simulator.(simulation_points);"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
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},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"histogram(simulation_output,xlabel=\"x\",ylabel=\"Count\",legend=false)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"gp = Kriging(simulation_points, simulation_output, lower_bound, upper_bound, p=[1.0, 5.0]);"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Out of sampling points\n"
]
},
{
"data": {
"text/plain": [
"((0.0, 300.0), 4.287590936164728)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"surrogate_optimize(simulator, SRBF(), lower_bound, upper_bound, gp, LatinHypercubeSample())"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 0.062837 seconds (104.80 k allocations: 5.534 MiB)\n"
]
}
],
"source": [
"@time gp_output = gp.(simulation_points);"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
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},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"scatter(simulation_output,gp_output,xlabel=\"Observed\",ylabel=\"Predicted\",legend=false,title=\"Training\")"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"n_valid = 10\n",
"validation_points = sample(n_valid, lower_bound, upper_bound, LatinHypercubeSample());\n",
"validation_output = simulator.(validation_points);"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"predictions = gp.(validation_points);"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
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},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"scatter(validation_output,predictions,xlabel=\"Observed\",ylabel=\"Predicted\",legend=false,title=\"Testing\")"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"n_predict = 10000\n",
"prediction_points = sample(n_predict, lower_bound, upper_bound, LatinHypercubeSample());"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"prediction_output = gp.(prediction_points);"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"prediction_se = std_error_at_point.(gp, prediction_points);"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"prediction_implausibility = abs.(prediction_output .- 2000)./(prediction_se .+ sqrt(400));"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
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},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sum(prediction_implausibility .> 3.0)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
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@vikram-s-narayan
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vikram-s-narayan commented Apr 10, 2022 •
edited
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@sdwfrost
A new surrogate - AbstractGPSurrogate - has been added to surrogates.jl.

The following code where we replace the Kriging surrogate with AbstractGPSurrogate:

using AbstractGPs #necessary to define kernel - GP(SqExponentialKernel())

gp = AbstractGPSurrogate(simulation_points, simulation_output, gp=GP(SqExponentialKernel()), Σy=0.01)
@time gp_output = gp.(simulation_points);
scatter(simulation_output,gp_output,xlabel="Observed",ylabel="Predicted",legend=false,title="Training")
n_valid = 10
validation_points = sample(n_valid, lower_bound, upper_bound, LatinHypercubeSample());
validation_output = simulator.(validation_points);
@time predictions = gp.(validation_points);
scatter(validation_output,predictions,xlabel="Observed",ylabel="Predicted",legend=false,title="Testing")
n_predict = 10000
prediction_points = sample(n_predict, lower_bound, upper_bound, LatinHypercubeSample());
prediction_output = gp.(prediction_points);
prediction_se = std_error_at_point.(gp, prediction_points);
prediction_implausibility = abs.(prediction_output .- 2000)./(prediction_se .+ sqrt(400));
sum(prediction_implausibility .> 3.0)
scatter(prediction_points,markersize=5.0,group=prediction_implausibility .< 3.0)

produces a plot like this:

Screenshot 2022-04-10 at 12 51 29 PM

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