Merge pull request #729 from sdesai1287/docs_update

Docs modifications to use QuadratureTraining instead of GridTraining

Project.toml

@@ -89,4 +89,4 @@ SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test", "CUDA", "SafeTestsets", "OptimizationOptimisers", "OptimizationOptimJL", "Pkg", "OrdinaryDiffEq", "IntegralsCuba"]
+test = ["Test", "CUDA", "SafeTestsets", "OptimizationOptimisers", "OptimizationOptimJL", "Pkg", "OrdinaryDiffEq", "IntegralsCuba"]

docs/src/tutorials/constraints.md

@@ -35,8 +35,6 @@ Dxx = Differential(x)^2
 _σ = 0.5
 x_0 = -2.2
 x_end = 2.2
-# Discretization
-dx = 0.01
 
 eq = Dx((α * x - β * x^3) * p(x)) ~ (_σ^2 / 2) * Dxx(p(x))
 
@@ -57,15 +55,15 @@ lb = [x_0]
 ub = [x_end]
 function norm_loss_function(phi, θ, p)
     function inner_f(x, θ)
-        dx * phi(x, θ) .- 1
+        0.01 * phi(x, θ) .- 1
     end
     prob = IntegralProblem(inner_f, lb, ub, θ)
     norm2 = solve(prob, HCubatureJL(), reltol = 1e-8, abstol = 1e-8, maxiters = 10)
     abs(norm2[1])
 end
 
 discretization = PhysicsInformedNN(chain,
-                                   GridTraining(dx),
+                                   QuadratureTraining(),
                                    additional_loss = norm_loss_function)
 
 @named pdesystem = PDESystem(eq, bcs, domains, [x], [p(x)])
@@ -98,7 +96,7 @@ using Plots
 C = 142.88418699042 #fitting param
 analytic_sol_func(x) = C * exp((1 / (2 * _σ^2)) * (2 * α * x^2 - β * x^4))
 
-xs = [infimum(d.domain):dx:supremum(d.domain) for d in domains][1]
+xs = [infimum(d.domain):0.01:supremum(d.domain) for d in domains][1]
 u_real = [analytic_sol_func(x) for x in xs]
 u_predict = [first(phi(x, res.u)) for x in xs]
 

docs/src/tutorials/derivative_neural_network.md

@@ -93,9 +93,9 @@ input_ = length(domains)
 n = 15
 chain = [Lux.Chain(Dense(input_, n, Lux.σ), Dense(n, n, Lux.σ), Dense(n, 1)) for _ in 1:7]
 
-grid_strategy = NeuralPDE.GridTraining(0.07)
+training_strategy = NeuralPDE.QuadratureTraining()
 discretization = NeuralPDE.PhysicsInformedNN(chain,
-                                             grid_strategy)
+                                             training_strategy)
 
 vars = [u1(t, x), u2(t, x), u3(t, x), Dxu1(t, x), Dtu1(t, x), Dxu2(t, x), Dtu2(t, x)]
 @named pdesystem = PDESystem(eqs_, bcs__, domains, [t, x], vars)

docs/src/tutorials/gpu.md

@@ -84,7 +84,7 @@ chain = Chain(Dense(3, inner, Lux.σ),
               Dense(inner, inner, Lux.σ),
               Dense(inner, 1))
 
-strategy = GridTraining(0.05)
+strategy = QuadratureTraining()
 ps = Lux.setup(Random.default_rng(), chain)[1]
 ps = ps |> ComponentArray |> gpu .|> Float64
 discretization = PhysicsInformedNN(chain,

docs/src/tutorials/integro_diff.md

@@ -57,7 +57,7 @@ bcs = [i(0.0) ~ 0.0]
 domains = [t ∈ Interval(0.0, 2.0)]
 chain = Chain(Dense(1, 15, Flux.σ), Dense(15, 1)) |> f64
 
-strategy_ = GridTraining(0.05)
+strategy_ = QuadratureTraining()
 discretization = PhysicsInformedNN(chain,
                                    strategy_)
 @named pde_system = PDESystem(eq, bcs, domains, [t], [i(t)])

docs/src/tutorials/low_level.md

@@ -35,12 +35,9 @@ bcs = [u(0, x) ~ -sin(pi * x),
 domains = [t ∈ Interval(0.0, 1.0),
     x ∈ Interval(-1.0, 1.0)]
 
-# Discretization
-dx = 0.05
-
 # Neural network
 chain = Lux.Chain(Dense(2, 16, Lux.σ), Dense(16, 16, Lux.σ), Dense(16, 1))
-strategy = NeuralPDE.GridTraining(dx)
+strategy = NeuralPDE.QuadratureTraining()
 
 indvars = [t, x]
 depvars = [u(t, x)]
@@ -79,7 +76,7 @@ And some analysis:
 ```@example low_level
 using Plots
 
-ts, xs = [infimum(d.domain):dx:supremum(d.domain) for d in domains]
+ts, xs = [infimum(d.domain):0.01:supremum(d.domain) for d in domains]
 u_predict_contourf = reshape([first(phi([t, x], res.u)) for t in ts for x in xs],
                              length(xs), length(ts))
 plot(ts, xs, u_predict_contourf, linetype = :contourf, title = "predict")

docs/src/tutorials/neural_adapter.md

@@ -67,7 +67,7 @@ function loss(cord, θ)
     chain2(cord, θ) .- phi(cord, res.u)
 end
 
-strategy = NeuralPDE.GridTraining(0.02)
+strategy = NeuralPDE.QuadratureTraining()
 
 prob_ = NeuralPDE.neural_adapter(loss, init_params2, pde_system, strategy)
 callback = function (p, l)
@@ -179,7 +179,7 @@ for i in 1:count_decomp
     bcs_ = create_bcs(domains_[1].domain, phi_bound)
     @named pde_system_ = PDESystem(eq, bcs_, domains_, [x, y], [u(x, y)])
     push!(pde_system_map, pde_system_)
-    strategy = NeuralPDE.GridTraining([0.1 / count_decomp, 0.1])
+    strategy = NeuralPDE.QuadratureTraining()
 
     discretization = NeuralPDE.PhysicsInformedNN(chains[i], strategy;
                                                  init_params = init_params[i])
@@ -243,10 +243,10 @@ callback = function (p, l)
 end
 
 prob_ = NeuralPDE.neural_adapter(losses, init_params2, pde_system_map,
-                                 NeuralPDE.GridTraining([0.1 / count_decomp, 0.1]))
+                                 NeuralPDE.QuadratureTraining())
 res_ = Optimization.solve(prob_, BFGS(); callback = callback, maxiters = 2000)
 prob_ = NeuralPDE.neural_adapter(losses, res_.minimizer, pde_system_map,
-                                 NeuralPDE.GridTraining([0.05 / count_decomp, 0.05]))
+                                 NeuralPDE.QuadratureTraining())
 res_ = Optimization.solve(prob_, BFGS(); callback = callback, maxiters = 1000)
 
 phi_ = NeuralPDE.get_phi(chain2)

docs/src/tutorials/param_estim.md

@@ -58,7 +58,7 @@ u0 = [1.0; 0.0; 0.0]
 tspan = (0.0, 1.0)
 prob = ODEProblem(lorenz!, u0, tspan)
 sol = solve(prob, Tsit5(), dt = 0.1)
-ts = [infimum(d.domain):dt:supremum(d.domain) for d in domains][1]
+ts = [infimum(d.domain):0.01:supremum(d.domain) for d in domains][1]
 function getData(sol)
     data = []
     us = hcat(sol(ts).u...)
@@ -113,7 +113,7 @@ Then finally defining and optimizing using the `PhysicsInformedNN` interface.
 
 ```@example param_estim
 discretization = NeuralPDE.PhysicsInformedNN([chain1, chain2, chain3],
-                                             NeuralPDE.GridTraining(dt), param_estim = true,
+                                             NeuralPDE.QuadratureTraining(), param_estim = true,
                                              additional_loss = additional_loss)
 @named pde_system = PDESystem(eqs, bcs, domains, [t], [x(t), y(t), z(t)], [σ_, ρ, β],
                               defaults = Dict([p .=> 1.0 for p in [σ_, ρ, β]]))
@@ -130,7 +130,7 @@ And then finally some analysis by plotting.
 
 ```@example param_estim
 minimizers = [res.u.depvar[depvars[i]] for i in 1:3]
-ts = [infimum(d.domain):(dt / 10):supremum(d.domain) for d in domains][1]
+ts = [infimum(d.domain):(0.001):supremum(d.domain) for d in domains][1]
 u_predict = [[discretization.phi[i]([t], minimizers[i])[1] for t in ts] for i in 1:3]
 plot(sol)
 plot!(ts, u_predict, label = ["x(t)" "y(t)" "z(t)"])

docs/src/tutorials/pdesystem.md

@@ -23,7 +23,7 @@ on the space domain:
 x \in [0, 1] \, , \ y \in [0, 1] \, ,
 ```
 
-with grid discretization `dx = 0.05` using physics-informed neural networks.
+Using physics-informed neural networks.
 
 ## Copy-Pasteable Code
 
@@ -52,7 +52,7 @@ chain = Lux.Chain(Dense(dim, 16, Lux.σ), Dense(16, 16, Lux.σ), Dense(16, 1))
 
 # Discretization
 dx = 0.05
-discretization = PhysicsInformedNN(chain, GridTraining(dx))
+discretization = PhysicsInformedNN(chain, QuadratureTraining())
 
 @named pde_system = PDESystem(eq, bcs, domains, [x, y], [u(x, y)])
 prob = discretize(pde_system, discretization)
@@ -122,9 +122,8 @@ Here, we build PhysicsInformedNN algorithm where `dx` is the step of discretizat
 `strategy` stores information for choosing a training strategy.
 
 ```@example poisson
-# Discretization
 dx = 0.05
-discretization = PhysicsInformedNN(chain, GridTraining(dx))
+discretization = PhysicsInformedNN(chain, QuadratureTraining())
 ```
 
 As described in the API docs, we now need to define the `PDESystem` and create PINNs