Integrate DeepBSDE.jl

[vboussange]

For now, the file DeepBSDE.jl is a copy from NeuralPDE.jl and is not included in HighDimPDE.jl. It needs to be included, and modified to accept PIDEProblem and return PIDESolution, as well as accompanied with tests.

[vboussange]

Work in progress on the branch https://github.com/SciML/HighDimPDE.jl/tree/NNPDENS_integration .

File DeepBSDE.jl has been renamed NNPDENS.jl, and a test file has been added.

@ChrisRackauckas, can you precise the meaning of the acronym NNPDENS and why the algorithm is not called DeepBSDE?

Also, can you better detail the option

HighDimPDE.jl/src/NNPDENS.jl

Line 33 in 7230576

give_limit = false,

and the related code

HighDimPDE.jl/src/NNPDENS.jl

Lines 143 to 213 in 7230576

	if iszero(dt) == true
	error("dt choice is required for upper and lower bound calculation ")
	end
	sdeProb = SDEProblem(μ , σ , x0 , tspan , noise_rate_prototype = zeros(Float32,d,d))
	output_func(sol,i) = (sol[end],false)
	ensembleprob = EnsembleProblem(sdeProb , output_func = output_func)
	sim_f = solve(ensembleprob, alg, ensemblealg, dt=dt, trajectories = trajectories_upper )
	Xn = reduce( vcat ,sim_f.u )
	Un = collect(g(X) for X in Xn)
	tspan_rev = (tspan[2] , tspan[1])
	sdeProb2 = SDEProblem(F, G, [Xn[1] ; Un[1]] ,tspan_rev, p3 , noise_rate_prototype=noise)
	function prob_func(prob,i,repeat)
	SDEProblem(prob.f , prob.g , [Xn[i] ; Un[i]] , prob.tspan , prob.p ,noise_rate_prototype = prob.noise_rate_prototype)
	end
	ensembleprob2 = EnsembleProblem(sdeProb2 , prob_func = prob_func , output_func = output_func)
	sim = solve(ensembleprob2, alg, ensemblealg, dt=dt, trajectories=trajectories_upper, output_func = output_func,save_everystep = false ,sensealg=TrackerAdjoint())
	function sol_high()
	map(sim.u) do u
	u[2]
	end
	end
	loss_() = sum(sol_high())/trajectories_upper
	ps = Flux.params(u0, σᵀ∇u...)
	cb = function ()
	l = loss_()
	true && println("Current loss is: $l")
	l < 1e-6 && Flux.stop()
	end
	dataS = Iterators.repeated((), maxiters_upper)
	Flux.train!(loss_, ps, dataS, ADAM(0.01); cb = cb)
	u_high = loss_()
	# Function to precalculate the f values over the domain
	function give_f_matrix(X,urange,σᵀ∇u,p,t)
	map(urange.urange) do u
	f(X,u,σᵀ∇u,p,t)
	end
	end
	#The Legendre transform that uses the precalculated f values.
	function legendre_transform(f_matrix , a , urange)
	le = a.*(collect(urange.urange)) .- f_matrix
	return maximum(le)
	end
	ts = tspan[1]:dt:tspan[2]
	function sol_low()
	map(1:trajectories_lower) do j
	u = u0(x0)[1]
	X = x0
	I = zero(eltype(u))
	Q = zero(eltype(u))
	for i in 1:length(ts)-1
	t = ts[i]
	_σᵀ∇u = σᵀ∇u([X ; 0.0f0])
	dW = sqrt(dt)*randn(d)
	u = u - f(X, u, _σᵀ∇u, p, t)*dt + _σᵀ∇u'*dW
	X = X .+ μ(X,p,t)*dt .+ σ(X,p,t)*dW
	f_matrix = give_f_matrix(X , u_domain, _σᵀ∇u, p, ts[i])
	a_ = A[findmax(collect(A).*u .- collect(legendre_transform(f_matrix, a, u_domain) for a in A))[2]]
	I = I + a_*dt
	Q = Q + exp(I)*legendre_transform(f_matrix, a_, u_domain)
	end
	I , Q , X
	end
	end
	u_low = sum(exp(I)*g(X) - Q for (I ,Q ,X) in sol_low())/(trajectories_lower)
	save_everystep ? iters : re1(p3)(x0)[1] , u_low , u_high

?
I am not sure to understand its purpose.

I am running into a problem with Zygote as I tried to get rid of the old Tracker dependency in NeuralPDE.jl . I might try to solve the problem next week - but please feel free to work on the branch.

[vboussange]

This issue is now replaced by SciML/NeuralPDE.jl#514.