Merge pull request #242 from SciML/update_doc_mtk_v5

Update docs MTK v5

Author: ChrisRackauckas

README.md

@@ -39,8 +39,8 @@ using NeuralPDE, Flux, ModelingToolkit, GalacticOptim, Optim, DiffEqFlux
 
 @parameters x y
 @variables u(..)
-@derivatives Dxx''~x
-@derivatives Dyy''~y
+Dxx = Differential(x)^2
+Dyy = Differential(y)^2
 
 # 2D PDE
 eq  = Dxx(u(x,y)) + Dyy(u(x,y)) ~ -sin(pi*x)*sin(pi*y)
@@ -58,7 +58,7 @@ dx = 0.1
 dim = 2 # number of dimensions
 chain = FastChain(FastDense(dim,16,Flux.σ),FastDense(16,16,Flux.σ),FastDense(16,1))
 
-discretization = PhysicsInformedNN(chain, GridTraining(dx=dx))
+discretization = PhysicsInformedNN(chain, GridTraining(dx))
 
 pde_system = PDESystem(eq,bcs,domains,[x,y],[u])
 prob = discretize(pde_system,discretization)

docs/src/pinn/3D.md

@@ -19,9 +19,9 @@ with physics-informed neural networks.
 # 3D PDE
 @parameters x y t
 @variables u(..)
-@derivatives Dxx''~x
-@derivatives Dyy''~y
-@derivatives Dt'~t
+Dxx = Differential(x)^2
+Dyy = Differential(y)^2
+Dt = Differential(t)
 
 # 3D PDE
 eq  = Dt(u(x,y,t)) ~ Dxx(u(x,y,t)) + Dyy(u(x,y,t))

docs/src/pinn/3rd.md

@@ -9,9 +9,9 @@ with grid discretization `dx = 0.1`. We will use physics-informed neural network
 ```julia
 @parameters x
 @variables u(..)
-@derivatives Dxxx'''~x
-@derivatives Dx'~x
 
+Dxxx = Differential(x)^3
+Dx = Differential(x)
 # ODE
 eq = Dxxx(u(x)) ~ cos(pi*x)
 

docs/src/pinn/debugging.md

@@ -8,10 +8,9 @@ using NeuralPDE, ModelingToolkit, Flux, DiffEqFlux, Zygote
 # 2d wave equation, neumann boundary condition
 @parameters x, t
 @variables u(..)
-@derivatives Dxx''~x
-@derivatives Dtt''~t
-@derivatives Dt'~t
-
+Dxx = Differential(x)^2
+Dtt = Differential(t)^2
+Dt = Differential(t)
 #2D PDE
 C=1
 eq  = Dtt(u(x,t)) ~ C^2*Dxx(u(x,t))

docs/src/pinn/fp.md

@@ -18,8 +18,8 @@ with Physics-Informed Neural Networks.
 # the example is taken from this article https://arxiv.org/abs/1910.10503
 @parameters x
 @variables p(..)
-@derivatives Dx'~x
-@derivatives Dxx''~x
+Dx = Differential(x)
+Dxx = Differential(x)^2
 
 #2D PDE
 α = 0.3

docs/src/pinn/ks.md

@@ -13,11 +13,11 @@ with physics-informed neural networks.
 ```julia
 @parameters x, t
 @variables u(..)
-@derivatives Dt'~t
-@derivatives Dx'~x
-@derivatives Dx2''~x
-@derivatives Dx3'''~x
-@derivatives Dx4''''~x
+Dt = Differential(t)
+Dx = Differential(x)
+Dx2 = Differential(x)^2
+Dx3 = Differential(x)^3
+Dx4 = Differential(x)^4
 
 α = 1
 β = 4

docs/src/pinn/low_level.md

@@ -9,9 +9,9 @@ with Physics-Informed Neural Networks. Here is an example of using the low-level
 ```julia
 @parameters t, x
 @variables u(..)
-@derivatives Dt'~t
-@derivatives Dx'~x
-@derivatives Dxx''~x
+Dt = Differential(t)
+Dx = Differential(x)
+Dxx = Differential(x)^2
 
 #2D PDE
 eq  = Dt(u(t,x)) + u(t,x)*Dx(u(t,x)) - (0.01/pi)*Dxx(u(t,x)) ~ 0

docs/src/pinn/poisson.md

@@ -21,8 +21,8 @@ using NeuralPDE, Flux, ModelingToolkit, GalacticOptim, Optim, DiffEqFlux
 using Plots
 @parameters x y
 @variables u(..)
-@derivatives Dxx''~x
-@derivatives Dyy''~y
+Dxx = Differential(x)^2
+Dyy = Differential(y)^2
 
 # 2D PDE
 eq  = Dxx(u(x,y)) + Dyy(u(x,y)) ~ -sin(pi*x)*sin(pi*y)

docs/src/pinn/system.md

@@ -17,10 +17,10 @@ with physics-informed neural networks.
 ```julia
 @parameters t, x
 @variables u1(..), u2(..), u3(..)
-@derivatives Dt'~t
-@derivatives Dtt''~t
-@derivatives Dx'~x
-@derivatives Dxx''~x
+Dt = Differential(t)
+Dtt = Differential(t)^2
+Dx = Differential(x)
+Dxx = Differential(x)^2
 
 eqs = [Dtt(u1(t,x)) ~ Dxx(u1(t,x)) + u3(t,x)*sin(pi*x),
        Dtt(u2(t,x)) ~ Dxx(u2(t,x)) + u3(t,x)*cos(pi*x),

docs/src/pinn/wave.md

@@ -12,9 +12,9 @@ Further, the solution of this equation with the given boundary conditions is pre
 ```julia
 @parameters t, x
 @variables u(..)
-@derivatives Dxx''~x
-@derivatives Dtt''~t
-@derivatives Dt'~t
+Dxx = Differential(x)^2
+Dtt = Differential(t)^2
+Dt = Differential(t)
 
 #2D PDE
 C=1