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[WIP]Debug errors in Kolmogorov Equations model #179

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Jun 19, 2020
Merged

[WIP]Debug errors in Kolmogorov Equations model #179

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322c283
Bug Fix in the code
ashutosh-b-b Jun 17, 2020
64e2ba9
Debug Kolmogorov Model
ashutosh-b-b Jun 18, 2020
282623a
Add CUDA to check GPU
ashutosh-b-b Jun 18, 2020
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2 changes: 1 addition & 1 deletion Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -7,6 +7,7 @@ version = "0.7.0"
AlgebraicMultigrid = "2169fc97-5a83-5252-b627-83903c6c433c"
ArbNumerics = "7e558dbc-694d-5a72-987c-6f4ebed21442"
BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
CUDAnative = "be33ccc6-a3ff-5ff2-a52e-74243cff1e17"
Cairo = "159f3aea-2a34-519c-b102-8c37f9878175"
CuArrays = "3a865a2d-5b23-5a0f-bc46-62713ec82fae"
Expand Down Expand Up @@ -78,7 +79,6 @@ MCMCChains = "3.0, 4.0"
Measurements = "2.1"
ModelingToolkit = "0.9, 0.10, 1.0, 2.0, 3.0"
NLsolve = "4.2"
NeuralNetDiffEq = "1.5"
Optim = "0.19, 0.20, 0.21"
OrdinaryDiffEq = "5.23"
ParameterizedFunctions = "4.2, 5.0"
Expand Down
21 changes: 15 additions & 6 deletions tutorials/models/08-kolmogorov_equations.jmd
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Expand Up @@ -7,7 +7,8 @@ author: Ashutosh Bharambe
using Flux, StochasticDiffEq
using NeuralNetDiffEq
using Plots
using Distributions
using CuArrays
using CUDA
```
## Introduction on Backward Kolmogorov Equations

Expand Down Expand Up @@ -81,13 +82,17 @@ trajectories = 100000
Now lets define our model m and the optimiser
```julia
m = Chain(Dense(d, 8, leakyrelu),Dense(8, 16, leakyrelu),Dense(16 , 8 , leakyrelu) , Dense(8 , 1))
m = fmap(cu , m)
use_gpu = false
if CUDA.functional() == true
m = fmap(CuArrays.cu , m)
use_gpu = true
end
opt = Flux.ADAM(0.01)
```
And then finally call the solver
```julia
sol = solve(prob, NeuralNetDiffEq.NNKolmogorov(m, opt, sdealg, ensemblealg), verbose = true, dt = dt,
dx = dx , trajectories = trajectories , abstol=1e-6, maxiters = 4200)
@time sol = solve(prob, NeuralNetDiffEq.NNKolmogorov(m, opt, sdealg, ensemblealg), verbose = true, dt = dt,
dx = dx , trajectories = trajectories , abstol=1e-6, maxiters = 4200 , use_gpu = use_gpu)
```
## Analyzing the solution
Now let us find a Monte-Carlo Solution and plot the both:
Expand All @@ -105,15 +110,19 @@ for x in x_out
ensembleprob_val = EnsembleProblem(prob , output_func = output_func )
sim_val = solve(ensembleprob_val, EM(), EnsembleThreads() , dt=0.01, trajectories=100000,adaptive=false)
s = reduce(hcat , sim_val.u)
global monte_carlo_sol = push!(monte_carlo_sol , mean(phi(s)))
mean_phi = sum(phi(s))/length(phi(s))
global monte_carlo_sol = push!(monte_carlo_sol , mean_phi)
end

```

##Plotting the Solutions
We should reshape the inputs and outputs to make it compatible with our model. This is the most important part. The algorithm gives a distributed function over all initial prices in the xspan.
```julia
x_model = reshape(x_out, 1 , size(x_out)[1])
m = fmap(cu , m)
if use_gpu == true
m = fmap(cpu , m)
end
y_out = m(x_model)
y_out = reshape(y_out , 13 , 1)
```
Expand Down