[ufechner7]

Closes #267. Supersedes #261, which is out of date with main and failed the KPS4 steady-state tests.

Summary

• find_steady_state! (KPS3 and KPS4) now solves with the TrustRegion solver of NonlinearSolve (radius update scheme NLsolve), through a small wrapper nl_solve in src/utils.jl. It returns the fields of the NLsolve result that find_steady_state! uses, so the retry and continuation logic is unchanged.
• Scaling is essential. NLsolve's autoscale (Moré column-norm scaling) is what makes it robust here. Without it, TrustRegion, Levenberg–Marquardt and Newton with backtracking each solve some cases and fail others. nl_solve scales the unknowns by the column norms of the Jacobian. NLsolve updates that scaling every iteration; here it is updated when the solver is restarted from its last iterate, up to 3 times.
• NLsolve and NLSolversBase are removed from Project.toml, test/Project.toml and test/create_sys_image.jl.

Benchmark

system.yaml, KPS4 and KPS3, with and without trim, v_wind 6/10/15/25 m/s, elevation 40/50/60/70/85°, l_tether 50/150/392/1000 m: 320 cases per solver, Julia 1.13.1.

Solver	KPS4 solved	KPS3 solved	Total time
NLsolve (main)	160/160	155/160	50 s
NonlinearSolve, no scaling	158/160	158/160	–
NonlinearSolve, fixed scaling	156/160	155/160	–
NonlinearSolve, scaling updated on restart (this PR)	160/160	155/160	152 s

• Same cases solved: this PR fails the same 5 KPS3 cases as NLsolve (25 m/s, no trim, 40–60°, 392/1000 m).
• Slower on hard cases: the median case is 1.8× slower. Hard cases fall through to the stiffness continuation and are 5–18× slower. The worst is KPS4 with trim at 6 m/s, 85° and 50 m: 9.7 s instead of 0.5 s. KPS4 with trim at 6 m/s and 1000 m takes about 5 s instead of 0.9 s.
• Different solutions at low elevations: without trim, NonlinearSolve lands on the deep-stall solution more often (KPS4: 31 cases instead of 25), so the winch force can differ by several kN.
• Bug on main, unchanged by this PR: KPS3 with trim=true at 6 m/s, 40° and 1000 m returns a trimmed state at −78° elevation with both solvers.

The slowdown is to be investigated before merging.

Benchmark script

# Compare the steady-state solvers (NLsolve vs NonlinearSolve) on a grid of cases
using KiteModels, KitePodModels, Logging, Test
set_data_path(joinpath(dirname(dirname(pathof(KiteModels))), "data"))

const WINDS  = (6.0, 10.0, 15.0, 25.0)
const ELEVS  = (40.0, 50.0, 60.0, 70.0, 85.0)
const LENGTHS = (50.0, 150.0, 392.0, 1000.0)

function make_model(model, v, el, l)
    set = deepcopy(load_settings("system.yaml"))
    set.v_wind = v; set.elevation = el; set.l_tethers[1] = l; set.l_tether = l
    model == :kps4 ? KPS4(KCU(set)) : KPS3(KCU(set))
end

# :ok, :noconv (warning "did not converge"), :error; plus time and some state metrics
function run_case(model, v, el, l, trim)
    s = make_model(model, v, el, l)
    logger = Test.TestLogger(min_level=Logging.Warn)
    status = :ok
    t = @elapsed try
        with_logger(logger) do
            find_steady_state!(s; trim)
        end
    catch e
        status = :error
    end
    msgs = [string(r.message) for r in logger.logs]
    any(m -> occursin("did not converge", m), msgs) && status == :ok && (status = :noconv)
    stall = any(m -> occursin("deep stall", m), msgs)
    el_res = status == :error ? NaN : rad2deg(calc_elevation(s))
    force  = status == :error ? NaN : winch_force(s)
    (; model, v, el, l, trim, status, stall, t, el_res, force)
end

function bench(models=(:kps4, :kps3))
    res = []
    for model in models, trim in (false, true), v in WINDS, el in ELEVS, l in LENGTHS
        KaimonGate.is_cancelled() && break
        KaimonGate.progress("$model trim=$trim v=$v el=$el l=$l ($(length(res)))")
        push!(res, run_case(model, v, el, l, trim))
    end
    res
end

summary(res) = [(m, tr, count(r -> r.status == :ok, rs), count(r -> r.status != :ok, rs), round(sum(r.t for r in rs) / length(rs), digits=3))
                for m in unique(r.model for r in res), tr in (false, true)
                for rs in [filter(r -> r.model == m && r.trim == tr, res)]]

Usage: res = bench(); summary(res)

Test plan

• test-steady-state-robustness.jl: 54/54
• test-steady-state-kps4.jl: 15/15
• test-kps3.jl: 154/154
• test-kps4.jl: 223/223
• test-aqua.jl: 9/9
• full test suite (CI)

🤖 Generated with Claude Code

[ufechner7]

Reported the slowdown upstream: SciML/NonlinearSolve.jl#1370 (related: SciML/NonlinearSolve.jl#425, autoscaling for TrustRegion).