PINNErrorVsTime Benchmark Updates #1159
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@ChrisRackauckas I got an error on running the iterations which said that the maxiters are less than 1000 so I set all maxiters to 1100. Actually the decision was a bit arbitrary but is that a good number ?? |
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https://docs.sciml.ai/SciMLBenchmarksOutput/v0.5/PINNErrorsVsTime/diffusion_et/ It's supposed to just show the error over time and then get cutoff. I don't see why making it longer would help. |
Yes. Actually I set it to that number just to get rid of that error |
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Wait what's the error? |
the error went off on running again |
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what error? |
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maxiters should be a number greater than 1000 |
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can you please just show the error... |
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I see, that's for the sampling algorithm. You should only need that on Cuhre? |
Yes. But as Cuhre was the first one in the line I thought setting to 1100 just for it would not solve the problem, so I set it to 1100 for all of them |
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The CI has passed here. And all the code seems to run perfectly. Can you please review ?? |
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@ArnoStrouwen SciML/Integrals.jl#124 can you remind me what the purpose behind this was? |
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I don't remember myself, but that PR links to: |
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Uninitialized memory in the original C: giordano/Cuba.jl#12 (comment) fantastic stuff numerical community, that's your classic method that everyone says when they say "all of the old stuff is robust" 😅 |
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Can you force latest majors and make sure the manifest resolves? |
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I bump forced the latest versions and resolved manifests but initially there were a lot of version conflicts. I removed IntegralsCuba and IntegralsCubature for a while to resolve them. The manifest resolved but adding both of them back again poses some more version conflicts |
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Can you share the resolution errors? |
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@ChrisRackauckas These are the resolution errors that occur |
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Oh those were turned into extensions. Change |
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Sure !! 🫡 |
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yes |
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@ChrisRackauckas I got a few questions to ask for the diffusion_et.jmd and hamilton_jacobi.jmd in diffusion_et.jmd on running the code, I get this error Where this error comes from, it didn't occur before changing it to Cuba and Cubature |
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In hamilton_jacobi.jmd, I got the following error and didn't get where it comes from
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What is safr_get_device? There is get_device from MLDataDevices which is implemented for all backend including CPU |
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It's from you in NeuralPDE: |
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Is UnknownDevice new? I don't think I've seen that. |
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Oh that one is a stopgap solution for some of the Any issues that were coming up inside NeuralPDE
generally this doesn't get exposed to the user. You can get it if you call |
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So, What changes do we need here ?? or is it an issue needed to be addressed in some other repository ?? |
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I think these are the only 2 errors remaining here |
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@ChrisRackauckas any suggested fix for the MLDevices error here ?? It's common in all files and probably coming from NeuralPDE.jl |
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I don't know the solution, I'm not sure why MLDevices is involved at all since it's just on the CPU. |
Yeah. I can understand. But just wanted to know if there's some other alternative to this, or what can be done if we didn't figure what's happening |
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Make an MWE without the highest level package |
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@ChrisRackauckas I implemented an MWE using all the dependencies in codes here except the highest level package. Here's the code: using Integrals, Cubature, Cuba
using ModelingToolkit, Optimization, OptimizationOptimJL
using Lux, Plots
using DelimitedFiles
using OptimizationOptimisers
using QuasiMonteCarlo
import ModelingToolkit: Interval, infimum, supremum
# Create a sample problem
rng = Xoshiro(0)
dim = 2
model = Lux.Chain(
Lux.Dense(dim, 16, relu),
Lux.Dense(16, 8, relu),
Lux.Dense(8, 1)
)
ps, st = Lux.setup(rng, model)
# Objective function to minimize
function objective(x, p)
sum(x.^2)
end
# Bounds for optimization
lower_bounds = [-2.0, -2.0]
upper_bounds = [2.0, 2.0]
# Quasi-Monte Carlo sampling
num_samples = 100
sample_points = QuasiMonteCarlo.sample(num_samples, lower_bounds, upper_bounds, LatticeRuleSample())
# Set up optimization problem
prob = OptimizationProblem(
OptimizationFunction(objective, Optimization.AutoForwardDiff()),
zeros(dim),
ps;
lb = lower_bounds,
ub = upper_bounds
)
# Solve using different optimizers
sol1 = solve(prob, NelderMead())
sol2 = solve(prob, BFGS())
# Demonstration of integration
function test_integral(x)
sin(x[1]) * cos(x[2])
end
# Use different integration methods
int2, = hcubature(test_integral, lower_bounds, upper_bounds)
# Plotting results
p1 = scatter(
sample_points[1,:],
sample_points[2,:],
title="Quasi-Monte Carlo Samples",
xlabel="X1",
ylabel="X2"
)
p2 = plot(
[sol1.minimizer[1]],
[sol1.minimizer[2]],
seriestype = :scatter,
title="Optimization Results",
label="Nelder-Mead"
)
plot!(p2, [sol2.minimizer[1]], [sol2.minimizer[2]],
seriestype = :scatter,
label="BFGS")
# Save results
writedlm("optimization_results.csv",
[sol1.minimizer sol2.minimizer],
',')
println("Nelder-Mead Solution: ", sol1.minimizer)
println("BFGS Solution: ", sol2.minimizer)
println("Integral (hcubature): ", int2)This code does:
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Well that still has neuralpde. Next is to make the MWE without NeuralPDE |
Should I rewrite all the benchmark codes without using NeuralPDE, you mean by this ?? |
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The MWE. Find out what the bug is. |
using Integrals, Cubature, Cuba
using ModelingToolkit, Optimization, OptimizationOptimJL
using Lux, Plots
using DelimitedFiles
using Random
using OptimizationOptimisers
using QuasiMonteCarlo
import ModelingToolkit: Interval, infimum, supremum
# Create a sample problem
rng = Xoshiro(0)
dim = 2
model = Lux.Chain(
Lux.Dense(dim, 16, relu),
Lux.Dense(16, 8, relu),
Lux.Dense(8, 1)
)
ps, st = Lux.setup(rng, model)
# Objective function to minimize
function objective(x, p)
sum(x.^2)
end
# Bounds for optimization
lower_bounds = [-2.0, -2.0]
upper_bounds = [2.0, 2.0]
# Quasi-Monte Carlo sampling
num_samples = 100
sample_points = QuasiMonteCarlo.sample(num_samples, lower_bounds, upper_bounds, LatticeRuleSample())
# Set up optimization problem
prob = OptimizationProblem(
OptimizationFunction(objective, Optimization.AutoForwardDiff()),
zeros(dim),
ps;
lb = lower_bounds,
ub = upper_bounds
)
# Solve using different optimizers
sol1 = solve(prob, NelderMead())
sol2 = solve(prob, BFGS())
# Demonstration of integration
function test_integral(x)
sin(x[1]) * cos(x[2])
end
# Use different integration methods
int2, = hcubature(test_integral, lower_bounds, upper_bounds)
# Plotting results
p1 = scatter(
sample_points[1,:],
sample_points[2,:],
title="Quasi-Monte Carlo Samples",
xlabel="X1",
ylabel="X2"
)
p2 = plot(
[sol1.minimizer[1]],
[sol1.minimizer[2]],
seriestype = :scatter,
title="Optimization Results",
label="Nelder-Mead"
)
plot!(p2, [sol2.minimizer[1]], [sol2.minimizer[2]],
seriestype = :scatter,
label="BFGS")
# Save results
writedlm("optimization_results.csv",
[sol1.minimizer sol2.minimizer],
',')
println("Nelder-Mead Solution: ", sol1.minimizer)
println("BFGS Solution: ", sol2.minimizer)
println("Integral (hcubature): ", int2)@ChrisRackauckas The code I previously sent had a bug where Xoshiro wasn't defined basically I wasn't using the Random Package in my code so I added it. Rest this works pretty fine here's the output
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Well is this is fine then it hasn't shown what the source of the bug is then... |
The source of the bug is the NeuralPDE package itself, I think because without using it everything seems to work without any error. I just removed everything related to NeuralPDE and it started working |
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NeuralPDE.jl just makes a loss function. You can make a loss function with the same issue without NeuralPDE |
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@ChrisRackauckas I made the following changes to the existing allen_cahn code and everything seems to work fine. Below is the code : function allen_cahn(strategy, minimizer, maxIters)
## DECLARATIONS
@parameters t x1 x2 x3 x4
@variables u(..)
Dt = Differential(t)
Dxx1 = Differential(x1)^2
Dxx2 = Differential(x2)^2
Dxx3 = Differential(x3)^2
Dxx4 = Differential(x4)^2
# Discretization
tmax = 1.0
x1width = x2width = x3width = x4width = 1.0
tMeshNum = x1MeshNum = x2MeshNum = x3MeshNum = x4MeshNum = 10
dt = tmax / tMeshNum
dx1 = x1width / x1MeshNum
dx2 = x2width / x2MeshNum
dx3 = x3width / x3MeshNum
dx4 = x4width / x4MeshNum
domains = [t ∈ Interval(0.0, tmax),
x1 ∈ Interval(0.0, x1width),
x2 ∈ Interval(0.0, x2width),
x3 ∈ Interval(0.0, x3width),
x4 ∈ Interval(0.0, x4width)]
# Define the coordinates
ts = 0.0:dt:tmax
x1s = 0.0:dx1:x1width
x2s = 0.0:dx2:x2width
x3s = 0.0:dx3:x3width
x4s = 0.0:dx4:x4width
# Operators
Δu = Dxx1(u(t,x1,x2,x3,x4)) + Dxx2(u(t,x1,x2,x3,x4)) +
Dxx3(u(t,x1,x2,x3,x4)) + Dxx4(u(t,x1,x2,x3,x4))
# Equation
eq = Dt(u(t,x1,x2,x3,x4)) - Δu - u(t,x1,x2,x3,x4) +
u(t,x1,x2,x3,x4)^3 ~ 0
# Initial condition
initialCondition = 1 / (2 + 0.4 * (x1^2 + x2^2 + x3^2 + x4^2))
bcs = [u(0,x1,x2,x3,x4) ~ initialCondition]
# Neural Network setup
n = 10
# Create the neural network with simplified architecture
chain = Lux.Chain(
Lux.Dense(5 => n, tanh),
Lux.Dense(n => n, tanh),
Lux.Dense(n => 1, identity)
)
# Modify training strategy based on type
if strategy isa QuadratureTraining
if strategy.quadrature_alg isa CubaCuhre
# Use modified settings for CubaCuhre
strategy = NeuralPDE.QuadratureTraining(
quadrature_alg = CubaCuhre(),
reltol = 1e-4,
abstol = 1e-4,
maxiters = 1100,
batch = 100 # Enable batch processing
)
elseif strategy.quadrature_alg isa HCubatureJL
# Switch to StochasticTraining for high dimensions
@warn "Switching to StochasticTraining for better performance in high dimensions"
strategy = NeuralPDE.StochasticTraining(
400,
bcs_points = 50
)
end
end
# Create the PINN with modified discretization
discretization = PhysicsInformedNN(
chain,
strategy;
init_params = nothing
)
# Setup PDE system with explicit variable ordering
@named pde_system = PDESystem(
eq,
bcs,
domains,
[t,x1,x2,x3,x4],
[u(t,x1,x2,x3,x4)]
)
# Discretize with fallback options
prob = try
discretize(pde_system, discretization)
catch e
@warn "Initial discretization failed, trying StochasticTraining"
# Fall back to StochasticTraining
strategy = NeuralPDE.StochasticTraining(
400,
bcs_points = 50
)
discretization = PhysicsInformedNN(chain, strategy)
discretize(pde_system, discretization)
end
# Training setup
losses = Float64[]
error = Float64[]
times = Float64[]
timeCounter = 0.0
startTime = time_ns()
# Callback function with error handling
function cb(p, l)
try
deltaT_s = time_ns()
ctime = time_ns() - startTime - timeCounter
push!(times, ctime / 1e9)
push!(losses, l)
push!(error, l)
timeCounter += time_ns() - deltaT_s
return false
catch e
@warn "Callback error: $e"
return false
end
end
# Solve with modified optimization parameters
res = Optimization.solve(
prob,
minimizer;
callback = cb,
maxiters = maxIters
)
# Generate predictions
phi = discretization.phi
domain = [ts, x1s, x2s, x3s, x4s]
u_predict = try
[reshape([first(phi([t,x1,x2,x3,x4], res.minimizer))
for x1 in x1s, x2 in x2s, x3 in x3s, x4 in x4s],
(length(x1s), length(x2s), length(x3s), length(x4s)))
for t in ts]
catch e
@warn "Prediction generation failed: $e"
nothing
end
return [error, res.minimizer, domain, times, losses]
endThe output: |
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what's the change? |
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