fix: Remove TerminalPDEProblem and replace with PIDEProblem

add a try catch because `f` is interpreted differently for DeepBSDE and
DeepSplitting

src/HighDimPDE.jl

@@ -75,8 +75,16 @@ module HighDimPDE
 
         isnothing(neumann_bc) ? nothing : @assert eltype(eltype(neumann_bc)) <: eltype(x)
         @assert eltype(g(x)) == eltype(x) "Type of `g(x)` must match type of x"
-        @assert(eltype(f(x, x, g(x), g(x), x, x, p, tspan[1])) == eltype(x),
+        try 
+            @assert(eltype(f(x, x, g(x), g(x), x, x, p, tspan[1])) == eltype(x),
             "Type of non linear function `f(x)` must type of x")
+        catch e 
+            if isa(e, MethodError)
+                    @assert(eltype(f(x, eltype(x)(0.0), x, p, tspan[1])) == eltype(x), "Type of non linear function `f(x)` must type of x")
+            else
+                throw(e)
+            end
+        end
 
         PIDEProblem{typeof(g(x)),
                     typeof(g),
@@ -92,56 +100,6 @@ module HighDimPDE
                     g(x), g, f, μ, σ, x, tspan, p, x0_sample, neumann_bc, kwargs)
     end
 
-    """
-    $(SIGNATURES)   
-
-    Defines a semilinear Partial Differential Equation Problem with terminal conditions, of the form 
-    ```math 
-    \\begin{aligned}
-        \\frac{du}{dt} &= \\tfrac{1}{2} \\text{Tr}(\\sigma \\sigma^T) \\Delta u(x, t) + \\mu \\nabla u(x, t) \\\\ 
-        &\\quad + f(x, u(x, t), ( \\nabla_x u )(x, t), p, t)
-    \\end{aligned}
-    ```
-    with `` u(x,T) = g(x)``.
-
-    ## Arguments
-
-    * `g` : The terminal condition, of the form `g(x, p, t)`.
-    * `f` : The nonlinear function, of the form `f(x, u(x, t), ∇u(x, t), p, t)`.
-    * `μ` : drift function, of the form `μ(x, p, t)`.
-    * `σ` : diffusion function `σ(x, p, t)`.
-    * `x`: point where `u(x,t)` is approximated. Is required even in the case where `x0_sample` is provided. Determines the dimensionality of the PDE.
-    * `tspan`: timespan of the problem.
-    * `p`: the parameter vector.
-    """
-    struct TerminalPDEProblem{G,F,Mu,Sigma,X,T,P,A,UD,NBC,K} <: AbstractPDEProblem
-        g::G
-        f::F
-        μ::Mu
-        σ::Sigma
-        x::X
-        tspan::Tuple{T,T}
-        p::P
-        A::A
-        x0_sample::UD # the domain of u to be solved
-        neumann_bc::NBC # neumann boundary conditions, for now not used
-        kwargs::K
-    end
-
-    function TerminalPDEProblem(g,f,μ,σ,x,tspan,p=nothing;A=nothing,x0_sample=nothing,neumann_bc=nothing,kwargs...)
-        TerminalPDEProblem{typeof(g),
-                            typeof(f),
-                            typeof(μ),
-                            typeof(σ),
-                            typeof(x),
-                            eltype(tspan),
-                            typeof(p),
-                            typeof(A),
-                            typeof(x0_sample),
-                            typeof(neumann_bc),
-                            typeof(kwargs)}(
-                            g,f,μ,σ,x,tspan,p,A,x0_sample,neumann_bc,kwargs)
-    end
     struct PIDESolution{X0,Ts,L,Us,NNs,Ls}
         x0::X0
         ts::Ts
@@ -177,7 +135,7 @@ module HighDimPDE
     include("DeepBSDE_Han.jl")
     include("MLP.jl")
 
-    export PIDEProblem, TerminalPDEProblem, PIDESolution, DeepSplitting, DeepBSDE, MLP
+    export PIDEProblem, PIDEProblem, PIDESolution, DeepSplitting, DeepBSDE, MLP
 
     export NormalSampling, UniformSampling, NoSampling, solve
 end