diff --git a/src/structural_transformation/utils.jl b/src/structural_transformation/utils.jl
index 8b2ac1f69c..bd24a1d017 100644
--- a/src/structural_transformation/utils.jl
+++ b/src/structural_transformation/utils.jl
@@ -58,7 +58,41 @@ end
 ###
 ### Structural check
 ###
-function check_consistency(state::TransformationState, orig_inputs)
+
+"""
+    $(TYPEDSIGNATURES)
+
+Check if the `state` represents a singular system, and return the unmatched variables.
+"""
+function singular_check(state::TransformationState)
+    @unpack graph, var_to_diff = state.structure
+    fullvars = get_fullvars(state)
+    # This is defined to check if Pantelides algorithm terminates. For more
+    # details, check the equation (15) of the original paper.
+    extended_graph = (@set graph.fadjlist = Vector{Int}[graph.fadjlist;
+                                                        map(collect, edges(var_to_diff))])
+    extended_var_eq_matching = maximal_matching(extended_graph)
+
+    nvars = ndsts(graph)
+    unassigned_var = []
+    for (vj, eq) in enumerate(extended_var_eq_matching)
+        vj > nvars && break
+        if eq === unassigned && !isempty(𝑑neighbors(graph, vj))
+            push!(unassigned_var, fullvars[vj])
+        end
+    end
+    return unassigned_var
+end
+
+"""
+    $(TYPEDSIGNATURES)
+
+Check the consistency of `state`, given the inputs `orig_inputs`. If `nothrow == false`,
+throws an error if the system is under-/over-determined or singular. In this case, if the
+function returns it will return `true`. If `nothrow == true`, it will return `false`
+instead of throwing an error. The singular case will print a warning.
+"""
+function check_consistency(state::TransformationState, orig_inputs; nothrow = false)
     fullvars = get_fullvars(state)
     neqs = n_concrete_eqs(state)
     @unpack graph, var_to_diff = state.structure
@@ -72,6 +106,7 @@ function check_consistency(state::TransformationState, orig_inputs)
     is_balanced = n_highest_vars == neqs
 
     if neqs > 0 && !is_balanced
+        nothrow && return false
         varwhitelist = var_to_diff .== nothing
         var_eq_matching = maximal_matching(graph, eq -> true, v -> varwhitelist[v]) # not assigned
         # Just use `error_reporting` to do conditional
@@ -85,22 +120,12 @@ function check_consistency(state::TransformationState, orig_inputs)
         error_reporting(state, bad_idxs, n_highest_vars, iseqs, orig_inputs)
     end
 
-    # This is defined to check if Pantelides algorithm terminates. For more
-    # details, check the equation (15) of the original paper.
-    extended_graph = (@set graph.fadjlist = Vector{Int}[graph.fadjlist;
-                                                        map(collect, edges(var_to_diff))])
-    extended_var_eq_matching = maximal_matching(extended_graph)
-
-    nvars = ndsts(graph)
-    unassigned_var = []
-    for (vj, eq) in enumerate(extended_var_eq_matching)
-        vj > nvars && break
-        if eq === unassigned && !isempty(𝑑neighbors(graph, vj))
-            push!(unassigned_var, fullvars[vj])
-        end
-    end
+    unassigned_var = singular_check(state)
 
     if !isempty(unassigned_var) || !is_balanced
+        if nothrow
+            return false
+        end
         io = IOBuffer()
         Base.print_array(io, unassigned_var)
         unassigned_var_str = String(take!(io))
@@ -110,7 +135,7 @@ function check_consistency(state::TransformationState, orig_inputs)
         throw(InvalidSystemException(errmsg))
     end
 
-    return nothing
+    return true
 end
 
 ###
diff --git a/src/systems/abstractsystem.jl b/src/systems/abstractsystem.jl
index 497b5e6476..3a9bbd33e1 100644
--- a/src/systems/abstractsystem.jl
+++ b/src/systems/abstractsystem.jl
@@ -3335,7 +3335,8 @@ function parse_variable(sys::AbstractSystem, str::AbstractString)
     # I'd write a regex to validate `str`, but https://xkcd.com/1171/
     str = strip(str)
     derivative_level = 0
-    while ((cond1 = startswith(str, "D(")) || startswith(str, "Differential(")) && endswith(str, ")")
+    while ((cond1 = startswith(str, "D(")) || startswith(str, "Differential(")) &&
+        endswith(str, ")")
         if cond1
             derivative_level += 1
             str = _string_view_inner(str, 2, 1)
diff --git a/src/systems/diffeqs/abstractodesystem.jl b/src/systems/diffeqs/abstractodesystem.jl
index 1dc2198cc2..5c13572aef 100644
--- a/src/systems/diffeqs/abstractodesystem.jl
+++ b/src/systems/diffeqs/abstractodesystem.jl
@@ -1295,7 +1295,7 @@ function InitializationProblem{iip, specialize}(sys::AbstractODESystem,
         check_length = true,
         warn_initialize_determined = true,
         initialization_eqs = [],
-        fully_determined = false,
+        fully_determined = nothing,
         check_units = true,
         kwargs...) where {iip, specialize}
     if !iscomplete(sys)
@@ -1313,6 +1313,19 @@ function InitializationProblem{iip, specialize}(sys::AbstractODESystem,
                 sys; u0map, initialization_eqs, check_units, pmap = parammap); fully_determined)
     end
 
+    ts = get_tearing_state(isys)
+    if warn_initialize_determined &&
+       (unassigned_vars = StructuralTransformations.singular_check(ts); !isempty(unassigned_vars))
+        errmsg = """
+        The initialization system is structurally singular. Guess values may \
+        significantly affect the initial values of the ODE. The problematic variables \
+        are $unassigned_vars.
+
+        Note that the identification of problematic variables is a best-effort heuristic.
+        """
+        @warn errmsg
+    end
+
     uninit = setdiff(unknowns(sys), [unknowns(isys); getfield.(observed(isys), :lhs)])
 
     # TODO: throw on uninitialized arrays
diff --git a/src/systems/problem_utils.jl b/src/systems/problem_utils.jl
index ff1d69e2bc..1cf110df13 100644
--- a/src/systems/problem_utils.jl
+++ b/src/systems/problem_utils.jl
@@ -498,7 +498,7 @@ function process_SciMLProblem(
         constructor, sys::AbstractSystem, u0map, pmap; build_initializeprob = true,
         implicit_dae = false, t = nothing, guesses = AnyDict(),
         warn_initialize_determined = true, initialization_eqs = [],
-        eval_expression = false, eval_module = @__MODULE__, fully_determined = false,
+        eval_expression = false, eval_module = @__MODULE__, fully_determined = nothing,
         check_initialization_units = false, tofloat = true, use_union = false,
         u0_constructor = identity, du0map = nothing, check_length = true,
         symbolic_u0 = false, warn_cyclic_dependency = false,
diff --git a/src/systems/systemstructure.jl b/src/systems/systemstructure.jl
index 71bdf6fe30..1c0ad8b8ae 100644
--- a/src/systems/systemstructure.jl
+++ b/src/systems/systemstructure.jl
@@ -677,7 +677,11 @@ function _structural_simplify!(state::TearingState, io; simplify = false,
         check_consistency = true, fully_determined = true, warn_initialize_determined = false,
         dummy_derivative = true,
         kwargs...)
-    check_consistency &= fully_determined
+    if fully_determined isa Bool
+        check_consistency &= fully_determined
+    else
+        check_consistency = true
+    end
     has_io = io !== nothing
     orig_inputs = Set()
     if has_io
@@ -690,7 +694,8 @@ function _structural_simplify!(state::TearingState, io; simplify = false,
     end
     sys, mm = ModelingToolkit.alias_elimination!(state; kwargs...)
     if check_consistency
-        ModelingToolkit.check_consistency(state, orig_inputs)
+        fully_determined = ModelingToolkit.check_consistency(
+            state, orig_inputs; nothrow = fully_determined === nothing)
     end
     if fully_determined && dummy_derivative
         sys = ModelingToolkit.dummy_derivative(
diff --git a/test/initializationsystem.jl b/test/initializationsystem.jl
index f39ec3c2f2..920a73a723 100644
--- a/test/initializationsystem.jl
+++ b/test/initializationsystem.jl
@@ -947,3 +947,14 @@ end
 
     @test_nowarn remake(prob, p = prob.p)
 end
+
+@testset "Singular initialization prints a warning" begin
+    @parameters g
+    @variables x(t) y(t) [state_priority = 10] λ(t)
+    eqs = [D(D(x)) ~ λ * x
+           D(D(y)) ~ λ * y - g
+           x^2 + y^2 ~ 1]
+    @mtkbuild pend = ODESystem(eqs, t)
+    @test_warn ["structurally singular", "initialization", "Guess", "heuristic"] ODEProblem(
+        pend, [x => 1, y => 0], (0.0, 1.5), [g => 1], guesses = [λ => 1])
+end