Replace NLsolve.jl with NonlinearSolve.jl TrustRegion

[ChrisRackauckas-Claude]

Summary

• Replaces NLsolve.jl trust region dogleg with NonlinearSolve.jl TrustRegion() in both KPS3 and KPS4 find_steady_state! functions
• Removes NLsolve and NLSolversBase as direct dependencies (NonlinearSolve was already a transitive dependency via OrdinaryDiffEqNonlinearSolve)
• Retains the custom finite-difference Jacobian (make_jac) since the model's MVector{3, Float64} internals cannot hold ForwardDiff.Dual numbers

Motivation

NLsolve.jl has known issues with subnormal Jacobian entries from NLSolversBase >= 7.10 (see PR #259). Rather than pinning NLSolversBase or maintaining workarounds, this PR switches to NonlinearSolve.jl which:

1. Already works — TrustRegion() passes all 452 tests (441 pass + 11 pre-existing broken)
2. Produces better results — On the l=392 steady-state test case, NonlinearSolve TrustRegion achieves 0.92% tether length error vs NLsolve's 1.35% (which fails the 1% rtol check)
3. Is faster — ~0.03s vs ~0.15s per solve (post-JIT)
4. Is already a dependency — No new packages added to the dependency tree
5. Doesn't need autoscale — NLsolve's autoscale=true (Moré/MINPACK diagonal scaling) is unnecessary with NonlinearSolve's TrustRegion

Changes

File	Change
src/KPS4.jl	Replace nlsolve() call with NonlinearProblem + solve(prob, TrustRegion())
src/KPS3.jl	Same replacement
src/KiteModels.jl	Remove NLsolve from using, add import SciMLBase
src/init.jl	Update make_jac docstring
Project.toml	Remove NLsolve/NLSolversBase deps, add SciMLBase
test/Project.toml	Remove NLsolve dep
examples_3d/Project.toml	Remove NLsolve dep
test/create_sys_image.jl	Remove NLsolve from sysimage

Test plan

• All 15 KPS4 steady-state tests pass
• All 67 KPS3 tests pass
• Full Pkg.test() passes: 441 pass + 11 pre-existing broken, 0 failures

Related

• NonlinearSolve.jl issue: Migration guide: NLsolve.nlsolve with manual Jacobian and autoscale for kite power system SciML/NonlinearSolve.jl#836
• KiteModels.jl PR Update NLSolve, fix NLsolve issue #259 (NLSolversBase subnormal workaround)

🤖 Generated with Claude Code

[ufechner7]

This branch is not passing the tests:

julia> include("test/test-steady-state-kps4.jl")
  Activating project at `~/repos/KiteModels.jl/test`
┌ Warning: find_steady_state!: solver did not converge! retcode=Stalled
└ @ KiteModels ~/repos/KiteModels.jl/src/KPS4.jl:704
test_find_steady_state: Test Failed at /home/ufechner/repos/KiteModels.jl/test/test-steady-state-kps4.jl:42
  Expression: pre_tension > 1.0001
   Evaluated: 1.0 > 1.0001

Stacktrace:
 [1] macro expansion
   @ ~/.julia/juliaup/julia-1.11.9+0.x64.linux.gnu/share/julia/stdlib/v1.11/Test/src/Test.jl:680 [inlined]
 [2] macro expansion
   @ ~/repos/KiteModels.jl/test/test-steady-state-kps4.jl:42 [inlined]
 [3] macro expansion
   @ ~/.julia/juliaup/julia-1.11.9+0.x64.linux.gnu/share/julia/stdlib/v1.11/Test/src/Test.jl:1709 [inlined]
 [4] top-level scope
   @ ~/repos/KiteModels.jl/test/test-steady-state-kps4.jl:30
┌ Warning: find_steady_state!: solver did not converge! retcode=MaxIters
└ @ KiteModels ~/repos/KiteModels.jl/src/KPS4.jl:704
test_find_steady_state: Test Failed at /home/ufechner/repos/KiteModels.jl/test/test-steady-state-kps4.jl:42
  Expression: pre_tension > 1.0001
   Evaluated: 1.0 > 1.0001

Stacktrace:
 [1] macro expansion
   @ ~/.julia/juliaup/julia-1.11.9+0.x64.linux.gnu/share/julia/stdlib/v1.11/Test/src/Test.jl:680 [inlined]
 [2] macro expansion
   @ ~/repos/KiteModels.jl/test/test-steady-state-kps4.jl:42 [inlined]
 [3] macro expansion
   @ ~/.julia/juliaup/julia-1.11.9+0.x64.linux.gnu/share/julia/stdlib/v1.11/Test/src/Test.jl:1709 [inlined]
 [4] top-level scope
   @ ~/repos/KiteModels.jl/test/test-steady-state-kps4.jl:30
test_find_steady_state: Test Failed at /home/ufechner/repos/KiteModels.jl/test/test-steady-state-kps4.jl:45
  Expression: isapprox(tether_length(kps4_local), 1.008954l, rtol = 0.01)
   Evaluated: isapprox(197.42057783848486, 201.7908; rtol = 0.01)

Stacktrace:
 [1] macro expansion
   @ ~/.julia/juliaup/julia-1.11.9+0.x64.linux.gnu/share/julia/stdlib/v1.11/Test/src/Test.jl:680 [inlined]
 [2] macro expansion
   @ ~/repos/KiteModels.jl/test/test-steady-state-kps4.jl:45 [inlined]
 [3] macro expansion
   @ ~/.julia/juliaup/julia-1.11.9+0.x64.linux.gnu/share/julia/stdlib/v1.11/Test/src/Test.jl:1709 [inlined]
 [4] top-level scope
   @ ~/repos/KiteModels.jl/test/test-steady-state-kps4.jl:30
┌ Warning: find_steady_state!: solver did not converge! retcode=MaxIters
└ @ KiteModels ~/repos/KiteModels.jl/src/KPS4.jl:704
test_find_steady_state: Test Failed at /home/ufechner/repos/KiteModels.jl/test/test-steady-state-kps4.jl:42
  Expression: pre_tension > 1.0001
   Evaluated: 1.0 > 1.0001

Stacktrace:
 [1] macro expansion
   @ ~/.julia/juliaup/julia-1.11.9+0.x64.linux.gnu/share/julia/stdlib/v1.11/Test/src/Test.jl:680 [inlined]
 [2] macro expansion
   @ ~/repos/KiteModels.jl/test/test-steady-state-kps4.jl:42 [inlined]
 [3] macro expansion
   @ ~/.julia/juliaup/julia-1.11.9+0.x64.linux.gnu/share/julia/stdlib/v1.11/Test/src/Test.jl:1709 [inlined]
 [4] top-level scope
   @ ~/repos/KiteModels.jl/test/test-steady-state-kps4.jl:30
test_find_steady_state: Test Failed at /home/ufechner/repos/KiteModels.jl/test/test-steady-state-kps4.jl:45
  Expression: isapprox(tether_length(kps4_local), 1.008954l, rtol = 0.01)
   Evaluated: isapprox(389.9800737647081, 395.50996799999996; rtol = 0.01)

Stacktrace:
 [1] macro expansion
   @ ~/.julia/juliaup/julia-1.11.9+0.x64.linux.gnu/share/julia/stdlib/v1.11/Test/src/Test.jl:680 [inlined]
 [2] macro expansion
   @ ~/repos/KiteModels.jl/test/test-steady-state-kps4.jl:45 [inlined]
 [3] macro expansion
   @ ~/.julia/juliaup/julia-1.11.9+0.x64.linux.gnu/share/julia/stdlib/v1.11/Test/src/Test.jl:1709 [inlined]
 [4] top-level scope
   @ ~/repos/KiteModels.jl/test/test-steady-state-kps4.jl:30
Test Summary:          | Pass  Fail  Total  Time
test_find_steady_state |   10     5     15  1.6s
ERROR: LoadError: Some tests did not pass: 10 passed, 5 failed, 0 errored, 0 broken.
in expression starting at /home/ufechner/repos/KiteModels.jl/test/test-steady-state-kps4.jl:29

[ChrisRackauckas]

v1.12 is fine but v1.11 is not. Peculiar.

[oscardssmith]

now that the linear solve issue is fixed we should rerun tests

[ChrisRackauckas-Claude]

Retested locally on Julia 1.11.9 with LinearSolve.jl v3.59.1 (which includes the fix from LinearSolve.jl#888). All tests pass:

Julia 1.11.9
LinearSolve v3.59.1
NonlinearSolve v4.16.0

Test Summary:               | Pass  Broken  Total     Time
Testing KiteModels...       |  441      11    452  1m22.0s
  Aqua                      |    9              9    27.5s
  Helpers                   |   19             19     1.3s
  Inertia Calculation       |   24             24     2.4s
  Interface                 |   14             14     0.7s
  Kps3 Fails                |    4              4     1.0s
  Kps3                      |   67             67     5.6s
  Kps4                      |  200      11    211    17.6s
  Orientation               |   81             81     1.0s
  Staticarrays              |    1              1     3.2s
  Steady State Kps4         |   15             15     0.4s
  KPS3 benchmarking....     |    2              2     4.1s
  KPS4 benchmarking...      |    5              5    16.7s

The root cause on 1.11 was LinearSolve.jl#887: MKLLUFactorization does in-place getrf! which corrupts cache.A with L\U factors. When LU fails on singular/rank-deficient Jacobians, DefaultLinearSolver's QR safety fallback got the corrupted matrix instead of the original, producing garbage Newton steps. This only affected Julia 1.11 (where MKL_jll loads) — on 1.12 MKL_jll doesn't load so the regular LUFactorization was used, which allocates a new object and leaves cache.A intact.

The fix in LinearSolve.jl#888 stores a backup of the original matrix and restores it before the QR fallback. With LinearSolve v3.59.1 this PR's KPS4 steady-state tests all converge correctly on Julia 1.11.