Support DiffCache in FullSpecialize initialization maps

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
Co-Authored-By: OpenAI Codex <noreply@openai.com>
Agent-Harness: Codex (version unknown)
Agent-Model: unknown
Agent-Session: local session ID 01a04feb-43da-7ce1-99e4-a68438c69833

Author: ChrisRackauckas

lib/ModelingToolkitBase/src/systems/parameter_buffer.jl

@@ -965,7 +965,7 @@ end
                     Expr(
                         :tuple,
                         (
-                            :($similar_type($(fieldtype(C, i)), $(nonnumericT[i]))(nonnumerics[$i]))
+                            :($similar_type($(fieldtype(N, i)), $(nonnumericT[i]))(nonnumerics[$i]))
                                 for i in 1:length(nonnumericT)
                         )...
                     )

lib/ModelingToolkitBase/src/systems/problem_utils.jl

@@ -1726,12 +1726,6 @@ function _construct_fullspecialize_initializeprobpmap(
             )
         )
     end
-    isempty(SU.getmetadata(sys, DiffCacheParams, Dict{SymbolicT, Int}())) || throw(
-        ArgumentError(
-            "FullSpecialize initialization maps do not yet support DiffCache parameters."
-        )
-    )
-
     expr = build_explicit_observed_function(
         initsys, Tuple(flat_syms);
         expression = Val(true), compiler_options, kwargs...