docs: use GridTraining for a couple examples which trains better and …

…faster
SciML · Mar 4, 2024 · 5fb889a · 5fb889a
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diff --git a/docs/src/examples/linear_parabolic.md b/docs/src/examples/linear_parabolic.md
@@ -24,7 +24,7 @@ w(t, 1) = \frac{e^{\lambda_1} cos(\frac{x}{a})-e^{\lambda_2}cos(\frac{x}{a})}{\l
 with a physics-informed neural network.
 
 ```@example
-using NeuralPDE, Lux, ModelingToolkit, Optimization, OptimizationOptimJL
+using NeuralPDE, Lux, ModelingToolkit, Optimization, OptimizationOptimJL, LineSearches
 using Plots
 import ModelingToolkit: Interval, infimum, supremum
 
@@ -71,7 +71,7 @@ input_ = length(domains)
 n = 15
 chain = [Lux.Chain(Dense(input_, n, Lux.σ), Dense(n, n, Lux.σ), Dense(n, 1)) for _ in 1:2]
 
-strategy = QuadratureTraining()
+strategy = GridTraining(0.01)
 discretization = PhysicsInformedNN(chain, strategy)
 
 @named pdesystem = PDESystem(eqs, bcs, domains, [t, x], [u(t, x), w(t, x)])
@@ -92,7 +92,7 @@ callback = function (p, l)
     return false
 end
 
-res = Optimization.solve(prob, BFGS(); callback = callback, maxiters = 5000)
+res = Optimization.solve(prob, LBFGS(linesearch = BackTracking()); callback = callback, maxiters = 500)
 
 phi = discretization.phi
 
@@ -110,9 +110,5 @@ for i in 1:2
     p2 = plot(ts, xs, u_predict[i], linetype = :contourf, title = "predict")
     p3 = plot(ts, xs, diff_u[i], linetype = :contourf, title = "error")
     plot(p1, p2, p3)
-    savefig("sol_u$i")
 end
 ```
-
-![linear_parabolic_sol_u1](https://user-images.githubusercontent.com/26853713/125745625-49c73760-0522-4ed4-9bdd-bcc567c9ace3.png)
-![linear_parabolic_sol_u2](https://user-images.githubusercontent.com/26853713/125745637-b12e1d06-e27b-46fe-89f3-076d415fcd7e.png)
diff --git a/docs/src/examples/nonlinear_elliptic.md b/docs/src/examples/nonlinear_elliptic.md
@@ -79,18 +79,14 @@ input_ = length(domains)
 n = 15
 chain = [Lux.Chain(Dense(input_, n, Lux.σ), Dense(n, n, Lux.σ), Dense(n, 1)) for _ in 1:6] # 1:number of @variables
 
-strategy = QuadratureTraining()
+strategy = GridTraining(0.01)
 discretization = PhysicsInformedNN(chain, strategy)
 
 vars = [u(x, y), w(x, y), Dxu(x, y), Dyu(x, y), Dxw(x, y), Dyw(x, y)]
 @named pdesystem = PDESystem(eqs_, bcs__, domains, [x, y], vars)
 prob = NeuralPDE.discretize(pdesystem, discretization)
 sym_prob = NeuralPDE.symbolic_discretize(pdesystem, discretization)
 
-strategy = NeuralPDE.QuadratureTraining()
-discretization = PhysicsInformedNN(chain, strategy)
-sym_prob = NeuralPDE.symbolic_discretize(pdesystem, discretization)
-
 pde_inner_loss_functions = sym_prob.loss_functions.pde_loss_functions
 bcs_inner_loss_functions = sym_prob.loss_functions.bc_loss_functions[1:6]
 aprox_derivative_loss_functions = sym_prob.loss_functions.bc_loss_functions[7:end]
@@ -107,7 +103,7 @@ callback = function (p, l)
     return false
 end
 
-res = Optimization.solve(prob, BFGS(); callback = callback, maxiters = 5000)
+res = Optimization.solve(prob, BFGS(); callback = callback, maxiters = 100)
 
 phi = discretization.phi
 
@@ -125,9 +121,5 @@ for i in 1:2
     p2 = plot(xs, ys, u_predict[i], linetype = :contourf, title = "predict")
     p3 = plot(xs, ys, diff_u[i], linetype = :contourf, title = "error")
     plot(p1, p2, p3)
-    savefig("non_linear_elliptic_sol_u$i")
 end
 ```
-
-![non_linear_elliptic_sol_u1](https://user-images.githubusercontent.com/26853713/125745550-0b667c10-b09a-4659-a543-4f7a7e025d6c.png)
-![non_linear_elliptic_sol_u2](https://user-images.githubusercontent.com/26853713/125745571-45a04739-7838-40ce-b979-43b88d149028.png)
diff --git a/docs/src/tutorials/constraints.md b/docs/src/tutorials/constraints.md
@@ -63,7 +63,7 @@ function norm_loss_function(phi, θ, p)
 end
 
 discretization = PhysicsInformedNN(chain,
-                                   QuadratureTraining(),
+                                   GridTraining(0.01),
                                    additional_loss = norm_loss_function)
 
 @named pdesystem = PDESystem(eq, bcs, domains, [x], [p(x)])
@@ -86,7 +86,7 @@ end
 
 res = Optimization.solve(prob, LBFGS(), callback = cb_, maxiters = 400)
 prob = remake(prob, u0 = res.u)
-res = Optimization.solve(prob, BFGS(), callback = cb_, maxiters = 2000)
+res = Optimization.solve(prob, BFGS(), callback = cb_, maxiters = 500)
 ```
 
 And some analysis:
@@ -103,5 +103,3 @@ u_predict = [first(phi(x, res.u)) for x in xs]
 plot(xs, u_real, label = "analytic")
 plot!(xs, u_predict, label = "predict")
 ```
-
-![fp](https://user-images.githubusercontent.com/12683885/129405830-3d00c24e-adf1-443b-aa36-6af0e5305821.png)