Restructure documentation (#507)

* Restructure documentation

Fixes #504

* fix typo

* another typo

Author: ChrisRackauckas

docs/make.jl

@@ -12,24 +12,37 @@ makedocs(
                              canonical="https://diffeqflux.sciml.ai/stable/"),
     pages=[
         "DiffEqFlux.jl: Generalized Physics-Informed and Scientific Machine Learning (SciML)" => "index.md",
-        "Basic Parameter Fitting Tutorials" => Any[
+        "Ordinary Differential Equation (ODE) Tutorials" => Any[
             "examples/optimization_ode.md",
-            "examples/optimization_sde.md",
-            "examples/lotka_volterra.md",
-            "examples/delay_diffeq.md",
-            "examples/pde_constrained.md",
             "examples/stiff_ode_fit.md",
-        ],
-        "Neural ODE and SDE Tutorials" => Any[
             "examples/neural_ode_sciml.md",
             "examples/neural_ode_flux.md",
             "examples/mnist_neural_ode.md",
-            "examples/neural_sde.md",
             "examples/augmented_neural_ode.md",
             "examples/collocation.md",
             "examples/neural_gde.md",
+            "examples/exogenous_input.md",
             "examples/normalizing_flows.md"
         ],
+
+        "Stochastic Differential Equation (SDE) Tutorials" => Any[
+            "examples/optimization_sde.md",
+            "examples/neural_sde.md",
+        ],
+        "Delay Differential Equation (DDE) Tutorials" => Any[
+            "examples/delay_diffeq.md",
+        ],
+        "Differential-Algebraic Equation (DAE) Tutorials" => Any[
+            "examples/physical_constraints.md",
+        ],
+        "Partial Differential Equation (PDE) Tutorials" => Any[
+            "examples/pde_constrained.md",
+        ],
+        "Hybrid and Jump Equation Tutorials" => Any[
+            "examples/hybrid_diffeq.md",
+            "examples/bouncing_ball.md",
+            "examples/jump.md",
+        ],
         "Bayesian Estimation Tutorials" => Any[
             "examples/turing_bayesian.md",
             "examples/BayesianNODE_NUTS.md",
@@ -43,20 +56,13 @@ makedocs(
             "examples/second_order_adjoints.md",
             "examples/minibatch.md",
         ],
-        "Hybrid and Jump Tutorials" => Any[
-            "examples/hybrid_diffeq.md",
-            "examples/bouncing_ball.md",
-            "examples/jump.md",
-        ],
         "Optimal and Model Predictive Control Tutorials" => Any[
             "examples/optimal_control.md",
             "examples/feedback_control.md",
             "examples/SDE_control.md",
         ],
-        "Universal Differential Equations and Physical Constraints Tutorials" => Any[
+        "Universal Differential Equations and Physical Layer Tutorials" => Any[
             "examples/universal_diffeq.md",
-            "examples/exogenous_input.md",
-            "examples/physical_constraints.md",
             "examples/tensor_layer.md",
             "examples/hamiltonian_nn.md"
         ],

docs/src/examples/lotka_volterra.md

@@ -1,6 +1,6 @@
-# Partial Differential Equation Constrained Optimization
+# Partial Differential Equation (PDE) Constrained Optimization
 
-This example uses a prediction model to optimize the one-dimensional Burgers' Equation.
+This example uses a prediction model to optimize the one-dimensional Heat Equation.
 (Step-by-step description below)
 
 ```julia
@@ -40,15 +40,15 @@ function d2dx(u,dx)
 end
 
 ## ODE description of the Physics:
-function burgers(u,p,t)
+function heat(u,p,t)
     # Model parameters
     a0, a1 = p
     dx,Nx = xtrs #[1.0,3.0,0.125,100]
     return 2.0*a0 .* u +  a1 .* d2dx(u, dx)
 end
 
 # Testing Solver on linear PDE
-prob = ODEProblem(burgers,u0,tspan,p)
+prob = ODEProblem(heat,u0,tspan,p)
 sol = solve(prob,Tsit5(), dt=dt,saveat=t);
 
 plot(x, sol.u[1], lw=3, label="t0", size=(800,500))
@@ -162,13 +162,13 @@ function d2dx(u,dx)
 end
 ```
 
-### Burgers' Differential Equation
+### Heat Differential Equation
 
 Next, we setup our desired set of equations in order to define our problem.
 
 ```julia
 ## ODE description of the Physics:
-function burgers(u,p,t)
+function heat(u,p,t)
     # Model parameters
     a0, a1 = p
     dx,Nx = xtrs #[1.0,3.0,0.125,100]
@@ -183,7 +183,7 @@ will compare to further on.
 
 ```julia
 # Testing Solver on linear PDE
-prob = ODEProblem(burgers,u0,tspan,p)
+prob = ODEProblem(heat,u0,tspan,p)
 sol = solve(prob,Tsit5(), dt=dt,saveat=t);
 
 plot(x, sol.u[1], lw=3, label="t0", size=(800,500))