docs: update examples

SciML · Mar 13, 2024 · b13f7c0 · b13f7c0
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diff --git a/docs/src/examples/linear_parabolic.md b/docs/src/examples/linear_parabolic.md
@@ -24,9 +24,9 @@ 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, LineSearches
+using NeuralPDE, Lux, ModelingToolkit, Optimization, OptimizationOptimisers, OptimizationOptimJL, LineSearches
 using Plots
-import ModelingToolkit: Interval, infimum, supremum
+using ModelingToolkit: Interval, infimum, supremum
 
 @parameters t, x
 @variables u(..), w(..)
@@ -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 = GridTraining(0.01)
+strategy = StochasticTraining(500)
 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, LBFGS(linesearch = BackTracking()); callback = callback, maxiters = 500)
+res = Optimization.solve(prob, OptimizationOptimisers.Adam(1e-2); callback = callback, maxiters = 10000)
 
 phi = discretization.phi
 

diff --git a/docs/src/examples/nonlinear_hyperbolic.md b/docs/src/examples/nonlinear_hyperbolic.md
@@ -33,7 +33,7 @@ where k is a root of the algebraic (transcendental) equation f(k) = g(k), j0 and
 We solve this with Neural:
 
 ```@example
-using NeuralPDE, Lux, ModelingToolkit, Optimization, OptimizationOptimJL, Roots
+using NeuralPDE, Lux, ModelingToolkit, Optimization, OptimizationOptimJL, Roots, LineSearches
 using SpecialFunctions
 using Plots
 import ModelingToolkit: Interval, infimum, supremum
@@ -99,7 +99,7 @@ callback = function (p, l)
  return false
 end
 
-res = Optimization.solve(prob, BFGS(); callback = callback, maxiters = 1000)
+res = Optimization.solve(prob, BFGS(linesearch = BackTracking()); callback = callback, maxiters = 200)
 
 phi = discretization.phi
 
@@ -117,9 +117,5 @@ 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("nonlinear_hyperbolic_sol_u$i")
 end
 ```
-
-![nonlinear_hyperbolic_sol_u1](https://user-images.githubusercontent.com/26853713/126457614-d19e7a4d-f9e3-4e78-b8ae-1e58114a744e.png)
-![nonlinear_hyperbolic_sol_u2](https://user-images.githubusercontent.com/26853713/126457617-ee26c587-a97f-4a2e-b6b7-b326b1f117af.png)