From a0e7b18d08d83fd17637fa7176bd995b034ad16f Mon Sep 17 00:00:00 2001
From: Aayush Sabharwal <aayush.sabharwal@gmail.com>
Date: Thu, 18 Jun 2026 16:52:40 +0530
Subject: [PATCH 1/3] refactor: update `solvable_graph` in
 `eliminate_perfect_aliases!`

---
 src/systems/alias_elimination.jl | 18 +++++++++++++++++-
 1 file changed, 17 insertions(+), 1 deletion(-)

diff --git a/src/systems/alias_elimination.jl b/src/systems/alias_elimination.jl
index b1ee9fe5fb..8f53f65399 100644
--- a/src/systems/alias_elimination.jl
+++ b/src/systems/alias_elimination.jl
@@ -147,7 +147,6 @@ function find_perfect_aliases!(
     (; sys, fullvars, structure) = state
     (; graph, solvable_graph, var_to_diff, state_priorities) = structure
 
-    @assert solvable_graph === nothing
     diff_to_var = invview(var_to_diff)
     aliases = Dict{Int, Int}()
     subs = Dict{SymbolicT, SymbolicT}()
@@ -236,6 +235,7 @@ function find_perfect_aliases!(
 
                 append!(eqs_to_substitute, 𝑑neighbors(graph, v))
                 BipartiteGraphs.set_neighbors!(BipartiteGraphs.invview(graph), v, ())
+                solvable_graph === nothing || BipartiteGraphs.set_neighbors!(BipartiteGraphs.invview(solvable_graph), v, ())
 
                 dv = var_to_diff[v]
                 while dv isa Int
@@ -244,6 +244,7 @@ function find_perfect_aliases!(
 
                     append!(eqs_to_substitute, 𝑑neighbors(graph, dv))
                     BipartiteGraphs.set_neighbors!(BipartiteGraphs.invview(graph), dv, ())
+                    solvable_graph === nothing || BipartiteGraphs.set_neighbors!(BipartiteGraphs.invview(solvable_graph), dv, ())
 
                     dv = var_to_diff[dv]
                 end
@@ -275,6 +276,10 @@ function find_perfect_aliases!(
                 push!(eqs_to_substitute, e)
                 Graphs.rem_edge!(graph, e, v)
                 Graphs.add_edge!(graph, e, target)
+                if solvable_graph !== nothing && Graphs.has_edge(solvable_graph, BipartiteEdge(e, v))
+                    Graphs.rem_edge!(solvable_graph, e, v)
+                    Graphs.add_edge!(solvable_graph, e, target)
+                end
             end
 
             dv = var_to_diff[v]
@@ -292,6 +297,10 @@ function find_perfect_aliases!(
                     push!(eqs_to_substitute, e)
                     Graphs.rem_edge!(graph, e, dv)
                     Graphs.add_edge!(graph, e, dtarget)
+                    if solvable_graph !== nothing && Graphs.has_edge(solvable_graph, BipartiteEdge(e, dv))
+                        Graphs.rem_edge!(solvable_graph, e, dv)
+                        Graphs.add_edge!(solvable_graph, e, dtarget)
+                    end
                 end
 
                 dv = var_to_diff[dv]
@@ -320,6 +329,9 @@ function find_perfect_aliases!(
             else
                 v_pin = pop!(irrs) # irreducible var to pin to 0
                 BipartiteGraphs.set_neighbors!(graph, ieq, [v_pin])
+                if solvable_graph !== nothing
+                    BipartiteGraphs.set_neighbors!(solvable_graph, ieq, [v_pin])
+                end
                 eqs[ieq] = fullvars[v_pin] ~ zero_sym
                 original_eqs[ieq] = fullvars[v_pin] ~ zero_sym
             end
@@ -360,6 +372,10 @@ function find_perfect_aliases!(
             𝑠neighbors(graph, e)
         )
         BipartiteGraphs.set_neighbors!(graph, e, new_row)
+        if solvable_graph !== nothing
+            filter!(v -> Graphs.has_edge(solvable_graph, BipartiteEdge(e, v)), new_row)
+            BipartiteGraphs.set_neighbors!(solvable_graph, e, new_row)
+        end
     end
 
     # After substitution, alias equations that connected a sticky non-target

From 8d3b7b7d1afe2d9edff0230873693173487a7212 Mon Sep 17 00:00:00 2001
From: Aayush Sabharwal <aayush.sabharwal@gmail.com>
Date: Thu, 18 Jun 2026 16:53:11 +0530
Subject: [PATCH 2/3] refactor: return elimination information from
 `eliminate_perfect_aliases!`

---
 src/systems/alias_elimination.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/systems/alias_elimination.jl b/src/systems/alias_elimination.jl
index 8f53f65399..b2e5887f98 100644
--- a/src/systems/alias_elimination.jl
+++ b/src/systems/alias_elimination.jl
@@ -37,7 +37,7 @@ function eliminate_perfect_aliases!(state::TearingState)
     old_to_new_eq, old_to_new_var = StateSelection.rm_eqs_vars!(
         state, eqs_to_rm, vars_to_rm; eqs_sorted_and_uniqued = true
     )
-    return nothing
+    return old_to_new_eq, old_to_new_var, aliases
 end
 
 """

From 3fdc8d74a5ef739b92ee5d1bff64721b8c03673a Mon Sep 17 00:00:00 2001
From: Aayush Sabharwal <aayush.sabharwal@gmail.com>
Date: Thu, 18 Jun 2026 16:53:44 +0530
Subject: [PATCH 3/3] refactor: rerun `eliminate_perfect_aliases!` after
 `alias_elimination!`

---
 src/systems/systemstructure.jl | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/src/systems/systemstructure.jl b/src/systems/systemstructure.jl
index ef8a4a8e77..7f8fe4b2a7 100644
--- a/src/systems/systemstructure.jl
+++ b/src/systems/systemstructure.jl
@@ -213,6 +213,9 @@ function _mtkcompile!(
     eliminate_perfect_aliases!(state)
     StateSelection.trivial_tearing!(state)
     sys, mm = ModelingToolkit.alias_elimination!(state; fully_determined, kwargs...)
+    old_to_new_eq, old_to_new_var, aliases = eliminate_perfect_aliases!(state)
+    sys = state.sys
+    mm = StateSelection.get_new_mm(aliases, old_to_new_eq, old_to_new_var, mm)
     if check_consistency
         fully_determined = StateSelection.check_consistency(
             state, orig_inputs; nothrow = fully_determined === nothing