Add reusable homotopy solver caches (#1100)

* Eliminate dense continuation step allocations

Avoid temporary reshape wrappers for dense AutoForwardDiff Jacobians and same-buffer restructure calls, with direct warmed allocation regressions.

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

* Cache ForwardDiff Jacobian destinations

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

* Avoid per-step continuation solution allocations

Run reusable continuation correctors to completion without materializing a solution on every step, while retaining full solution construction for custom, bounded, and wrapper caches.

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

* Add reusable homotopy solver caches

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

* Add allocation-free nonlinear cache driver

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

* Guard the cache driver iterator contract

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

---------

Co-authored-by: ChrisRackauckas-Claude <accounts@chrisrackauckas.com>

Author: ChrisRackauckas-Claude

Project.toml

@@ -1,6 +1,6 @@
 name = "NonlinearSolve"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
-version = "4.23.2"
+version = "4.24.0"
 authors = ["SciML"]
 
 [deps]
@@ -98,7 +98,7 @@ NLSolvers = "0.5"
 NLsolve = "4.5"
 NaNMath = "1"
 NonlinearProblemLibrary = "0.1.2"
-NonlinearSolveBase = "2.37"
+NonlinearSolveBase = "2.40"
 NonlinearSolveFirstOrder = "2"
 NonlinearSolveQuasiNewton = "1.12"
 NonlinearSolveSpectralMethods = "1.6"

docs/src/devdocs/algorithm_helpers.md

@@ -62,6 +62,7 @@ NonlinearSolveFirstOrder.GenericTrustRegionScheme
 ```@docs
 NonlinearSolveBase.callback_into_cache!
 NonlinearSolveBase.concrete_jac
+NonlinearSolveBase.solve_cache!
 NonlinearSolveBase.assert_extension_supported_termination_condition
 NonlinearSolveBase.construct_extension_function_wrapper
 NonlinearSolveBase.construct_extension_jac

lib/NonlinearSolveBase/Project.toml

@@ -1,6 +1,6 @@
 name = "NonlinearSolveBase"
 uuid = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
-version = "2.39.0"
+version = "2.40.0"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
 
 [deps]

lib/NonlinearSolveBase/src/NonlinearSolveBase.jl

@@ -106,7 +106,10 @@ include("solve.jl")
 include("forward_diff.jl")
 
 # Unexported Public API
-@compat(public, (L2_NORM, Linf_NORM, NAN_CHECK, UNITLESS_ABS2, get_tolerance))
+@compat(
+    public,
+    (L2_NORM, Linf_NORM, NAN_CHECK, UNITLESS_ABS2, get_tolerance, solve_cache!)
+)
 
 @compat(public, (get_abstol, get_reltol))
 @compat(public, (AbstractNonlinearTerminationMode, AbstractSafeNonlinearTerminationMode))

lib/NonlinearSolveBase/src/arclength.jl

@@ -829,10 +829,10 @@ function CommonSolve.solve(
         # and discovers the winner) instead of re-failing the cheaper ladder members
         # on every warm-started step.
         reinit_retaining!(corr_cache, xpred)
-        last_sol = CommonSolve.solve!(corr_cache)
+        last_sol = _solve_without_solution!(corr_cache)
 
-        if SciMLBase.successful_retcode(last_sol)
-            xnew = last_sol.u
+        if _solve_result_successful(last_sol)
+            xnew = _solve_result_u(last_sol)
             # realized chord, built in the (currently free) secant scratch
             @. tscratch = xnew - xcur
             nchord = _theta_norm(tscratch, wu, wλ, n)
@@ -892,7 +892,8 @@ function CommonSolve.solve(
             # sweep — see `_effort_growth_factor`), giving the arclength driver an effort
             # signal alongside the purely geometric bend-angle test.
             if alg.adaptive
-                nit = last_sol.stats === nothing ? -1 : Int(last_sol.stats.nsteps)
+                result_stats = _solve_result_stats(last_sol)
+                nit = result_stats === nothing ? -1 : Int(result_stats.nsteps)
                 if _effort_wants_shrink(nit, budget)
                     ds / 2 >= min_ds && (ds = ds / 2)
                     streak = 0
@@ -913,7 +914,8 @@ function CommonSolve.solve(
         else
             return build_solution_less_specialize(
                 prob, alg, u, nothing;
-                retcode = last_sol.retcode, original = last_sol,
+                retcode = _solve_result_retcode(last_sol),
+                original = _solve_result_original(last_sol),
                 store_original = alg.store_original
             )
         end

lib/NonlinearSolveBase/src/forward_diff.jl

@@ -11,6 +11,9 @@ get_u(cache::NonlinearSolveForwardDiffCache) = get_u(cache.cache)
 get_fu(cache::NonlinearSolveForwardDiffCache) = get_fu(cache.cache)
 set_fu!(cache::NonlinearSolveForwardDiffCache, fu) = set_fu!(cache.cache, fu)
 SciMLBase.set_u!(cache::NonlinearSolveForwardDiffCache, u) = SciMLBase.set_u!(cache.cache, u)
+function _solve_without_solution!(cache::NonlinearSolveForwardDiffCache)
+    return CommonSolve.solve!(cache)
+end
 function NonlinearSolveBase.get_abstol(cache::NonlinearSolveForwardDiffCache)
     return NonlinearSolveBase.get_abstol(cache.cache)
 end