Doyle-Fuller-Newman (DFN) Battery Model Initialization
These benchmarks compares the runtime and error for a range of nonlinear solvers. The solvers are implemented in NonlinearProblemLibrary.jl, where you can find the problem function declarations. We test the following solvers:
- NonlinearSolve.jl's Newton Raphson method (
NewtonRaphson()). - NonlinearSolve.jl's Newton trust region method (
TrustRegion()). - NonlinearSolve.jl's Levenberg-Marquardt method (
LevenbergMarquardt()). - NonlinearSolve.jl's Broyden method (
Broyden()). - MINPACK's Modified Powell method (
CMINPACK(method=:hybr)). - MINPACK's Levenberg-Marquardt method (
CMINPACK(method=:lm)). - NLsolveJL's Newton Raphson (
NLsolveJL(method=:newton)). - NLsolveJL's Newton trust region (
NLsolveJL()). - NLsolveJL's Anderson acceleration (
NLsolveJL(method=:anderson)). - Sundials's Newton-Krylov method (
KINSOL()).
Setup
Fetch required packages.
using NonlinearSolve, LinearSolve, StaticArrays, Sundials, SpeedMapping,
BenchmarkTools, LinearAlgebra, DiffEqDevTools, PolyesterForwardDiff, CairoMakie,
RecursiveFactorization, Enzyme
import MINPACK, NLsolve, PETSc
import LineSearches
const RUS = RadiusUpdateSchemes;Declare the benchmarked solvers (and their names and plotting options).
HagerZhang() = LineSearchesJL(; method = LineSearches.HagerZhang())
MoreThuente() = LineSearchesJL(; method = LineSearches.MoreThuente())
GC.enable(false) # for PETSc
solvers_all = [
(; pkg = :nonlinearsolve, name = "Default PolyAlgorithm",
solver = Dict(:alg => FastShortcutNonlinearPolyalg(; autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve, name = "Newton Raphson",
solver = Dict(:alg => NewtonRaphson(; autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve,
name = "Newton Raphson (HagerZhang LineSearch)",
solver = Dict(:alg => NewtonRaphson(; linesearch = HagerZhang(), autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve,
name = "Newton Raphson (MoreThuente LineSearch)",
solver = Dict(:alg => NewtonRaphson(; linesearch = MoreThuente(), autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve,
name = "Newton Raphson (BackTracking LineSearch)",
solver = Dict(:alg => NewtonRaphson(; linesearch = BackTracking(), autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve,
name = "Newton Krylov with GMRES",
solver = Dict(:alg => NewtonRaphson(; linsolve = KrylovJL_GMRES(), autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve, name = "DFSane", solver = Dict(:alg => DFSane())),
(; pkg = :nonlinearsolve, name = "Trust Region",
solver = Dict(:alg => TrustRegion(; autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve,
name = "Trust Region (NLsolve Update)",
solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.NLsolve, autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve,
name = "Trust Region (Nocedal Wright)",
solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.NocedalWright, autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve,
name = "Trust Region (Hei)",
solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Hei, autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve,
name = "Trust Region (Yuan)",
solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Yuan, autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve,
name = "Trust Region (Bastin)",
solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Bastin, autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve,
name = "Trust Region (Fan)",
solver = Dict(:alg => TrustRegion(; radius_update_scheme = RUS.Fan, autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve, name = "Levenberg-Marquardt",
solver = Dict(:alg => LevenbergMarquardt(; autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve,
name = "Levenberg-Marquardt with Cholesky",
solver = Dict(:alg => LevenbergMarquardt(;
linsolve = CholeskyFactorization(), autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve,
name = "Levenberg-Marquardt (No Geodesic Accln.)",
solver = Dict(:alg => LevenbergMarquardt(; disable_geodesic = Val(true), autodiff = AutoEnzyme()))),
(; pkg = :nonlinearsolve,
name = "Levenberg-Marquardt (No Geodesic Accln.) with Cholesky",
solver = Dict(:alg => LevenbergMarquardt(; disable_geodesic = Val(true),
linsolve = CholeskyFactorization(), autodiff = AutoEnzyme()))), (;
pkg = :wrapper, name = "Newton Raphson [Sundials]",
solver = Dict(:alg => KINSOL(; linear_solver = :LapackDense, maxsetupcalls = 1))),
(; pkg = :wrapper,
name = "Newton Krylov [Sundials]",
solver = Dict(:alg => KINSOL(; linear_solver = :GMRES, maxsetupcalls = 1, krylov_dim = 1000))),
(; pkg = :wrapper,
name = "Newton Raphson with LineSearch [Sundials]",
solver = Dict(:alg => KINSOL(; globalization_strategy = :LineSearch, maxsetupcalls = 1))), (;
pkg = :wrapper, name = "Newton Raphson [NLsolve.jl]",
solver = Dict(:alg => NLsolveJL(; method = :newton, autodiff = :forward))),
(; pkg = :wrapper, name = "Trust Region [NLsolve.jl]",
solver = Dict(:alg => NLsolveJL(; autodiff = :forward))), (;
pkg = :wrapper, name = "Modified Powell [MINPACK]",
solver = Dict(:alg => CMINPACK(; method = :hybr))),
(; pkg = :wrapper, name = "Levenberg-Marquardt [MINPACK]",
solver = Dict(:alg => CMINPACK(; method = :lm))), (;
pkg = :wrapper, name = "Speed Mapping [SpeedMapping.jl]",
solver = Dict(:alg => SpeedMappingJL())),
(; pkg = :wrapper,
name = "Newton Raphson [PETSc]",
solver = Dict(:alg => PETScSNES(; snes_type = "newtonls", snes_linesearch_type = "basic"))),
(; pkg = :wrapper,
name = "Newton Raphson with QR [PETSc]",
solver = Dict(:alg => PETScSNES(;
snes_type = "newtonls", snes_linesearch_type = "basic", pc_type = "qr"))),
(; pkg = :wrapper, name = "Newton Raphson with BackTracking [PETSc]",
solver = Dict(:alg => PETScSNES(; snes_type = "newtonls"))),
(; pkg = :wrapper, name = "Newton Raphson with BackTracking & QR [PETSc]",
solver = Dict(:alg => PETScSNES(; snes_type = "newtonls", pc_type = "qr"))),
(; pkg = :wrapper, name = "Trust Region [PETSc]",
solver = Dict(:alg => PETScSNES(; snes_type = "newtontr"))),
(; pkg = :wrapper,
name = "Newton Krylov with GMRES [PETSc]",
solver = Dict(:alg => PETScSNES(;
snes_type = "newtonls", snes_linesearch_type = "basic",
ksp_type = "gmres", ksp_gmres_restart = 1000)))
];Setup the problem
function f!(out, u, p = nothing)
out[1] = -u[33]
out[2] = -u[32]
out[3] = -u[31]
out[4] = 1.9876764062810574e10(u[1] + u[4]) - 1.9876764062810574e10u[23]
out[5] = -u[2] + (-1.5546404484393263e-11exp(-19.460872248113507(-0.4 - u[10] + u[26])))
out[6] = -1.9876764062810574e10u[14] + 1.9876764062810574e10(u[3] + u[6])
out[7] = -1.9876764062810574e10u[4] +
114676.11822324689(-exp(-19.460872248113507(-0.6608489145760508 + u[25])) +
exp(19.460872248113507(-0.6608489145760508 + u[25])))
out[8] = -1.9876764062810574e10u[12] + 1.9876764062810574e10(u[2] + u[5])
out[9] = -1.9876764062810574e10u[6] +
114676.1182232469(-exp(-19.460872248113507(-0.6608489145760508 - u[11] +
u[27])) +
exp(19.460872248113507(-0.6608489145760508 - u[11] + u[27])))
out[10] = -4.284490145672665e10u[19] + 4.284490145672665e10(u[31] + u[7])
out[11] = -4.284490145672665e10u[21] + 4.284490145672665e10(u[32] + u[8])
out[12] = -4.284490145672665e10u[22] + 4.284490145672665e10(u[33] + u[9])
out[13] = 0.025692579121085843(7.680104664733624e7(u[10] - u[11]) +
7.680104664733624e7u[10]) - 1.793773306620288e9u[12]
out[14] = -u[3] +
(-1.5546404484393263e-11exp(-19.460872248113507(-0.4 - u[11] + u[27])))
out[15] = -1.9876764062810574e10u[5] +
114676.1182232469(-exp(-19.460872248113507(-0.6608489145760506 - u[10] +
u[26])) +
exp(19.460872248113507(-0.6608489145760506 - u[10] +
u[26])))
out[16] = 0.025692579121085843(7.680104664733624e7(-u[10] + u[11]) +
1.4529008434739566e8(u[11] - u[13])) -
1.793773306620288e9u[14]
out[17] = -1.793773306620288e9u[14] - 1.4404300298567445e9(-u[26] + u[27])
out[18] = 0.025692579121085843(5.1142109690283257e8(-u[11] + u[13]) +
4.7254130462088e9(u[13] - u[15]))
out[19] = 0.025692579121085843(4.7254130462088e9(-u[13] + u[15]) +
4.7254130462088e9(u[15] - u[16]))
out[20] = 0.025692579121085843(4.7254130462088e9(-u[15] + u[16]) +
2.3040372207628164e8(u[16] - u[17]))
out[21] = 0.025692579121085843(7.200116314883803e7(-u[16] + u[17]) +
3.6900178974461965e7(u[17] - u[18])) -
2.193876971198113e9u[19]
out[22] = -4.284490145672665e10u[7] +
147554.10828979727(-exp(-19.460872248113507(-3.3618450059739535 - u[17] +
u[28])) +
exp(19.460872248113507(-3.3618450059739535 - u[17] +
u[28])))
out[23] = 0.025692579121085843(3.6900178974461965e7(-u[17] + u[18]) +
3.6900178974461965e7(u[18] - u[20])) -
2.193876971198113e9u[21]
out[24] = -4.284490145672665e10u[8] +
147554.10828979727(-exp(-19.460872248113507(-3.3618450059739535 - u[18] +
u[29])) +
exp(19.460872248113507(-3.3618450059739535 - u[18] +
u[29])))
out[25] = 948060.7678835923(-u[18] + u[20]) - 2.193876971198113e9u[22]
out[26] = -u[1] + (-1.5546404484393263e-11exp(-19.460872248113507(-0.4 + u[25])))
out[27] = -2.193876971198113e9u[22] +
0.025692579121085843(-37499.99999999999u[24] -
8.296874999999998e10(-u[29] + u[30]))
out[28] = -1.793773306620288e9u[23] +
0.025692579121085843(34090.90909090909u[24] -
5.6064049586776855e10(u[25] - u[26]))
out[29] = -1.793773306620288e9u[12] +
0.025692579121085843(-5.6064049586776855e10(-u[25] + u[26]) -
5.6064049586776855e10(u[26] - u[27]))
out[30] = -2.193876971198113e9u[19] - 2.1316811739525905e9(u[28] - u[29])
out[31] = -2.193876971198113e9u[21] +
0.025692579121085843(-8.296874999999998e10(-u[28] + u[29]) -
8.296874999999998e10(u[29] - u[30]))
out[32] = -4.284490145672665e10u[9] +
147554.10828979727(-exp(-19.460872248113507(-3.3618450059739535 - u[20] +
u[30])) +
exp(19.460872248113507(-3.3618450059739535 - u[20] +
u[30])))
out[33] = 292.3000724036127 + u[24]
nothing
end
n = 1
x_sol = [
-3.889310081682032e-13,
-5.690845522092043e-13,
-1.4900105367898274e-12,
-2.1680981422696e-5,
-3.284624075480569e-5,
-8.820027287447222e-5,
9.53999632159426e-5,
2.1138249693289567e-5,
1.1829446876191545e-5,
0.019709320908045884,
0.06927785744111935,
-3.2846241323890243e-5,
0.13786323434647954,
-8.820027436448276e-5,
0.14528607936456214,
0.15270892438264475,
0.3049460860584471,
0.3812355737657502,
9.53999632159426e-5,
0.40860971681949443,
2.1138249693289567e-5,
1.1829446876191545e-5,
-2.1680981811627007e-5,
-292.3000724036127,
0.5895178515117894,
0.5896685912243755,
0.5897784273806014,
3.837532182598256,
3.8376303660343676,
3.837750304468262,
0.0,
0.0,
0.0
]
x_start = zeros(length(x_sol))
x_start[25:27] .= 0.6608489145760508
x_start[28:30] .= 3.3618450059739433
dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Doyle-Fuller-Newman (DFN) Battery Model Initialization")
testcase = (; prob = NonlinearProblem(f!, dict["start"]), true_sol = dict["sol"])(prob = SciMLBase.NonlinearProblem{Vector{Float64}, true, SciMLBase.NullPar
ameters, SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, typeof
(Main.var"##WeaveSandBox#225".f!), LinearAlgebra.UniformScaling{Bool}, Noth
ing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing
, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, No
thing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciML
Base.StandardNonlinearProblem, Nothing, Nothing}(SciMLBase.NonlinearFunctio
n{true, SciMLBase.FullSpecialize, typeof(Main.var"##WeaveSandBox#225".f!),
LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Not
hing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT
_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing}(Main.var"##WeaveSan
dBox#225".f!, LinearAlgebra.UniformScaling{Bool}(true), nothing, nothing, n
othing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, SciM
LBase.DEFAULT_OBSERVED_NO_TIME, nothing, nothing, nothing, nothing), [0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.6608489145760508, 0.
6608489145760508, 0.6608489145760508, 3.3618450059739433, 3.361845005973943
3, 3.3618450059739433, 0.0, 0.0, 0.0], SciMLBase.NullParameters(), SciMLBas
e.StandardNonlinearProblem(), nothing, nothing, Base.Pairs{Symbol, Union{},
Tuple{}, @NamedTuple{}}()), true_sol = [-3.889310081682032e-13, -5.6908455
22092043e-13, -1.4900105367898274e-12, -2.1680981422696e-5, -3.284624075480
569e-5, -8.820027287447222e-5, 9.53999632159426e-5, 2.1138249693289567e-5,
1.1829446876191545e-5, 0.019709320908045884 … -292.3000724036127, 0.58951
78515117894, 0.5896685912243755, 0.5897784273806014, 3.837532182598256, 3.8
376303660343676, 3.837750304468262, 0.0, 0.0, 0.0])Sets tolerances.
abstols = 1.0 ./ 10.0 .^ (3:0.5:6)
reltols = 1.0 ./ 10.0 .^ (3:0.5:6);Prepares various helper functions for benchmarking a specific problem.
function log_msg(msg; kwargs...)
if startswith(msg, "[Info]")
@info msg
elseif startswith(msg, "[Warn]")
@warn msg
elseif startswith(msg, "[Error]")
@error msg
else
@info msg
end
Base.printstyled(msg; kwargs...)
return
end
function check_solver(prob, solver)
try
sol = solve(prob.prob, solver.solver[:alg]; abstol = 1e-4, reltol = 1e-4,
maxiters = 10000)
err = norm(sol.resid, Inf)
if !SciMLBase.successful_retcode(sol.retcode)
log_msg(
"[Warn] Solver $(solver.name) returned retcode $(sol.retcode) with an residual norm = $(norm(sol.resid)).\n";
color = :red)
return false
elseif err > 1e3
log_msg(
"[Warn] Solver $(solver.name) had a very large residual (norm = $(norm(sol.resid))).\n";
color = :red)
return false
elseif isinf(err) || isnan(err)
log_msg("[Warn] Solver $(solver.name) had a residual of $(err).\n";
color = :red)
return false
end
log_msg(
"[Info] Solver $(solver.name) successfully solved the problem (norm = $(norm(sol.resid))).\n";
color = :green)
catch e
log_msg("[Warn] Solver $(solver.name) threw an error: $e.\n"; color = :red)
return false
end
return true
end
function generate_wpset(prob, solvers)
# Finds the solvers that can solve the problem
successful_solvers = filter(solver -> check_solver(prob, solver), solvers)
return WorkPrecisionSet(prob.prob, abstols, reltols,
getfield.(successful_solvers, :solver);
names = getfield.(successful_solvers, :name), numruns = 50, error_estimate = :l∞,
maxiters = 10000, verbose = true),
successful_solvers
endgenerate_wpset (generic function with 1 method)Benchmarks
We here run benchmarks for each of the solvers.
Problem
wp_set, successful_solvers = generate_wpset(testcase, solvers_all);[Info] Solver Default PolyAlgorithm successfully solved the problem (norm =
1.5941038377860503e-6).
[Info] Solver Newton Raphson successfully solved the problem (norm = 1.5941
038377860503e-6).
[Warn] Solver Newton Raphson (HagerZhang LineSearch) returned retcode MaxIt
ers with an residual norm = 196.3434605041991.
[Warn] Solver Newton Raphson (MoreThuente LineSearch) returned retcode MaxI
ters with an residual norm = 208.56523082587998.
[Warn] Solver Newton Raphson (BackTracking LineSearch) returned retcode Max
Iters with an residual norm = 205.06578094165897.
[Warn] Solver Newton Krylov with GMRES returned retcode Unstable with an re
sidual norm = 292.3000724036127.
[Warn] Solver DFSane returned retcode Stalled with an residual norm = 292.3
000724036127.
[Info] Solver Trust Region successfully solved the problem (norm = 6.873726
32864865e-7).
[Info] Solver Trust Region (NLsolve Update) successfully solved the problem
(norm = 1.594082102773168e-6).
[Info] Solver Trust Region (Nocedal Wright) successfully solved the problem
(norm = 1.5941545843685634e-6).
[Info] Solver Trust Region (Hei) successfully solved the problem (norm = 6.
9564285784738e-7).
[Warn] Solver Trust Region (Yuan) returned retcode MaxIters with an residua
l norm = 35.36932960756202.
[Info] Solver Trust Region (Bastin) successfully solved the problem (norm =
7.521057027826631e-7).
[Info] Solver Trust Region (Fan) successfully solved the problem (norm = 1.
5942247231853775e-6).
[Info] Solver Levenberg-Marquardt successfully solved the problem (norm = 7
.38426369554924e-5).
[Warn] Solver Levenberg-Marquardt with Cholesky returned retcode Stalled wi
th an residual norm = 0.0003179815605994228.
[Info] Solver Levenberg-Marquardt (No Geodesic Accln.) successfully solved
the problem (norm = 5.246607252366464e-7).
[Warn] Solver Levenberg-Marquardt (No Geodesic Accln.) with Cholesky return
ed retcode InternalLinearSolveFailed with an residual norm = 0.000301547349
8789062.
[Info] Solver Newton Raphson [Sundials] successfully solved the problem (no
rm = 1.6205733409240167e-6).
[Warn] Solver Newton Krylov [Sundials] had a very large residual (norm = In
f).
[Warn] Solver Newton Raphson with LineSearch [Sundials] returned retcode Fa
ilure with an residual norm = 203.8024932082229.
[Info] Solver Newton Raphson [NLsolve.jl] successfully solved the problem (
norm = 1.5941104186169045e-6).
[Info] Solver Trust Region [NLsolve.jl] successfully solved the problem (no
rm = 6.940612093440701e-7).
[Warn] Solver Modified Powell [MINPACK] returned retcode Failure with an re
sidual norm = 292.3000724036127.
[Warn] Solver Levenberg-Marquardt [MINPACK] returned retcode Failure with a
n residual norm = 292.3000724036127.
[Warn] Solver Speed Mapping [SpeedMapping.jl] returned retcode Failure with
an residual norm = 773.9600302958914.
[Warn] Solver Newton Raphson [PETSc] returned retcode Failure with an resid
ual norm = 8.918598151838181e8.
[Warn] Solver Newton Raphson with QR [PETSc] returned retcode Failure with
an residual norm = 9.003593553788315e8.
[Warn] Solver Newton Raphson with BackTracking [PETSc] returned retcode Fai
lure with an residual norm = 280.83522493021263.
[Warn] Solver Newton Raphson with BackTracking & QR [PETSc] returned retcod
e Failure with an residual norm = 280.8407454935218.
[Warn] Solver Trust Region [PETSc] returned retcode Failure with an residua
l norm = 202.00730475517162.
[Warn] Solver Newton Krylov with GMRES [PETSc] returned retcode Failure wit
h an residual norm = 8.918598151838181e8.Plot and Save the Plot
fig = begin
LINESTYLES = Dict(:nonlinearsolve => :solid, :simplenonlinearsolve => :dash,
:wrapper => :dot)
ASPECT_RATIO = 0.7
WIDTH = 1200
HEIGHT = round(Int, WIDTH * ASPECT_RATIO)
STROKEWIDTH = 2.5
colors = cgrad(:tableau_20, length(successful_solvers); categorical = true)
cycle = Cycle([:marker], covary = true)
plot_theme = Theme(Lines = (; cycle), Scatter = (; cycle))
idxs = sortperm(median.(getfield.(wp_set.wps, :times)))
with_theme(plot_theme) do
fig = Figure(; size = (WIDTH, HEIGHT))
# `textbf` doesn't work
ax = Axis(fig[1, 1], ylabel = L"Time $\mathbf{(s)}$",
xlabelsize = 22, ylabelsize = 22,
xlabel = L"Error: $\mathbf{||f(u^\ast)||_\infty}$",
xscale = log10, yscale = log10, xtickwidth = STROKEWIDTH,
ytickwidth = STROKEWIDTH, spinewidth = STROKEWIDTH,
xticklabelsize = 20, yticklabelsize = 20)
ls, scs = [], []
for (i, (wp, solver)) in enumerate(zip(wp_set.wps[idxs], successful_solvers[idxs]))
(; name, times, errors) = wp
errors = [err.l∞ for err in errors]
l = lines!(ax, errors, times; linestyle = LINESTYLES[solver.pkg], label = name,
linewidth = 5, color = colors[i])
sc = scatter!(
ax, errors, times; label = name, markersize = 16, strokewidth = 3,
color = colors[i])
push!(ls, l)
push!(scs, sc)
end
axislegend(ax, [[l, sc] for (l, sc) in zip(ls, scs)],
[solver.name for solver in successful_solvers[idxs]], "Successful Solvers";
framevisible = true, framewidth = STROKEWIDTH, orientation = :vertical,
titlesize = 20, nbanks = 1, labelsize = 16,# margin = (0.0, 80.0, 0.0, 0.0),
tellheight = false, tellwidth = true, patchsize = (40.0f0, 20.0f0),
position = :rb)
fig[0, :] = Label(fig,
"Doyle-Fuller-Newman (DFN) Battery Model Initialization: Work Precision Diagram",
fontsize = 24, tellwidth = false, font = :bold)
fig
end
end
save("battery_problem_work_precision.svg", fig)CairoMakie.Screen{SVG}Summary of successful solvers
Finally, we print a summary of which solvers successfully solved which problems.
solver_successes = [(solver in successful_solvers) ? "✔" : "✖" for solver in solvers_all];using PrettyTables
io = IOBuffer()
println(io, "```@raw html")
pretty_table(io, reshape(solver_successes, 1, :); backend = Val(:html),
header = getfield.(solvers_all, :name), alignment = :c)
println(io, "```")
Docs.Text(String(take!(io)))Error: TypeError: in keyword argument backend, expected Symbol, got a value of type Val{:html}
Appendix
These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.
To locally run this benchmark, do the following commands:
using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/NonlinearProblem","nonlinear_battery_problem.jmd")Computer Information:
Julia Version 1.10.10
Commit 95f30e51f41 (2025-06-27 09:51 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 128 × AMD EPYC 7502 32-Core Processor
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
Threads: 1 default, 0 interactive, 1 GC (on 128 virtual cores)
Environment:
JULIA_CPU_THREADS = 128
JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953:
Package Information:
Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/NonlinearProblem/Project.toml`
[2169fc97] AlgebraicMultigrid v1.2.0
[6e4b80f9] BenchmarkTools v1.6.3
[13f3f980] CairoMakie v0.15.8
[2b5f629d] DiffEqBase v6.210.0
[f3b72e0c] DiffEqDevTools v2.49.0
[a0c0ee7d] DifferentiationInterface v0.7.16
[7da242da] Enzyme v0.13.129
[40713840] IncompleteLU v0.2.1
[b964fa9f] LaTeXStrings v1.4.0
⌃ [d3d80556] LineSearches v7.5.1
[7ed4a6bd] LinearSolve v3.59.1
[4854310b] MINPACK v1.3.0
[2774e3e8] NLsolve v4.5.1
[b7050fa9] NonlinearProblemLibrary v0.1.4
[8913a72c] NonlinearSolve v4.16.0
[ace2c81b] PETSc v0.4.6
[98d1487c] PolyesterForwardDiff v0.1.3
[08abe8d2] PrettyTables v3.2.3
[f2c3362d] RecursiveFactorization v0.2.26
[31c91b34] SciMLBenchmarks v0.1.3
[efcf1570] Setfield v1.1.2
[727e6d20] SimpleNonlinearSolve v2.11.0
[9f842d2f] SparseConnectivityTracer v1.2.1
⌃ [0a514795] SparseMatrixColorings v0.4.23
[f1835b91] SpeedMapping v0.4.1
[860ef19b] StableRNGs v1.0.4
[90137ffa] StaticArrays v1.9.17
[c3572dad] Sundials v5.1.0
⌃ [0c5d862f] Symbolics v7.15.2
Info Packages marked with ⌃ have new versions available and may be upgradable.And the full manifest:
Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/NonlinearProblem/Manifest.toml`
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[70df07ce] BracketingNonlinearSolve v1.10.0
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⌃ [d3d80556] LineSearches v7.5.1
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[05181044] RelocatableFolders v1.0.1
[ae029012] Requires v1.3.1
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⌅ [1270edf5] x264_jll v10164.0.1+0
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[8ba89e20] Distributed
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[9fa8497b] Future
[b77e0a4c] InteractiveUtils
[4af54fe1] LazyArtifacts
[b27032c2] LibCURL v0.6.4
[76f85450] LibGit2
[8f399da3] Libdl
[37e2e46d] LinearAlgebra
[56ddb016] Logging
[d6f4376e] Markdown
[a63ad114] Mmap
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.10.0
[de0858da] Printf
[9abbd945] Profile
[3fa0cd96] REPL
[9a3f8284] Random
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization
[1a1011a3] SharedArrays
[6462fe0b] Sockets
[2f01184e] SparseArrays v1.10.0
[10745b16] Statistics v1.10.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test
[cf7118a7] UUIDs
[4ec0a83e] Unicode
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[deac9b47] LibCURL_jll v8.4.0+0
[e37daf67] LibGit2_jll v1.6.4+0
[29816b5a] LibSSH2_jll v1.11.0+1
[c8ffd9c3] MbedTLS_jll v2.28.2+1
[14a3606d] MozillaCACerts_jll v2023.1.10
[4536629a] OpenBLAS_jll v0.3.23+4
[05823500] OpenLibm_jll v0.8.5+0
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.2.1+1
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.52.0+1
[3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`