From 66db48ff0393b17e88e1887e67c6d17e4a855aad Mon Sep 17 00:00:00 2001
From: Sathvik Bhagavan <sathvik.bhagavan@juliahub.com>
Date: Tue, 12 Mar 2024 04:46:48 +0000
Subject: [PATCH] docs: use BFGS with back tracking for low level system
 tutorial

---
 docs/src/tutorials/low_level.md | 7 +++----
 docs/src/tutorials/pdesystem.md | 2 +-
 2 files changed, 4 insertions(+), 5 deletions(-)

diff --git a/docs/src/tutorials/low_level.md b/docs/src/tutorials/low_level.md
index d625bbcf0..63fa0d476 100644
--- a/docs/src/tutorials/low_level.md
+++ b/docs/src/tutorials/low_level.md
@@ -13,7 +13,7 @@ u(t, -1) = u(t, 1) = 0 \, ,
 with Physics-Informed Neural Networks. Here is an example of using the low-level API:
 
 ```@example low_level
-using NeuralPDE, Lux, ModelingToolkit, Optimization, OptimizationOptimJL
+using NeuralPDE, Lux, ModelingToolkit, Optimization, OptimizationOptimJL, LineSearches
 using ModelingToolkit: Interval, infimum, supremum
 
 @parameters t, x
@@ -37,7 +37,7 @@ domains = [t ∈ Interval(0.0, 1.0),
 
 # Neural network
 chain = Lux.Chain(Dense(2, 16, Lux.σ), Dense(16, 16, Lux.σ), Dense(16, 1))
-strategy = NeuralPDE.QuadratureTraining()
+strategy = NeuralPDE.QuadratureTraining(; abstol = 1e-6, reltol = 1e-6, batch = 200)
 
 indvars = [t, x]
 depvars = [u(t, x)]
@@ -67,8 +67,7 @@ end
 f_ = OptimizationFunction(loss_function, Optimization.AutoZygote())
 prob = Optimization.OptimizationProblem(f_, sym_prob.flat_init_params)
 
-res = Optimization.solve(prob, OptimizationOptimJL.BFGS(); callback = callback,
-                         maxiters = 2000)
+res = Optimization.solve(prob, BFGS(linesearch = BackTracking()); callback = callback, maxiters = 3000)
 ```
 
 And some analysis:
diff --git a/docs/src/tutorials/pdesystem.md b/docs/src/tutorials/pdesystem.md
index d5962f8d1..4076bce5c 100644
--- a/docs/src/tutorials/pdesystem.md
+++ b/docs/src/tutorials/pdesystem.md
@@ -66,7 +66,7 @@ end
 
 # Optimizer
 opt = OptimizationOptimJL.LBFGS(linesearch = BackTracking())
-res = solve(prob, opt, callback = callback, maxiters = 2000)
+res = solve(prob, opt, callback = callback, maxiters = 1000)
 phi = discretization.phi
 
 dx = 0.05