diff --git a/Project.toml b/Project.toml
index c7057a507..db4821fd5 100644
--- a/Project.toml
+++ b/Project.toml
@@ -102,8 +102,6 @@ OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
 PartialFunctions = "570af359-4316-4cb7-8c74-252c00c2016b"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
-PyCall = "438e738f-606a-5dbb-bf0a-cddfbfd45ab0"
-PythonCall = "6099a3de-0909-46bc-b1f4-468b9a2dfc0d"
 RCall = "6f49c342-dc21-5d91-9882-a32aef131414"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 Serialization = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
@@ -116,4 +114,4 @@ UnicodePlots = "b8865327-cd53-5732-bb35-84acbb429228"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Pkg", "Plots", "UnicodePlots", "PyCall", "PythonCall", "SafeTestsets", "Serialization", "Test", "StableRNGs", "StaticArrays", "StochasticDiffEq", "Aqua", "Zygote", "PartialFunctions", "DataFrames", "OrdinaryDiffEq", "ForwardDiff", "Tables"]
+test = ["Pkg", "Plots", "UnicodePlots", "SafeTestsets", "Serialization", "Test", "StableRNGs", "StaticArrays", "StochasticDiffEq", "Aqua", "Zygote", "PartialFunctions", "DataFrames", "OrdinaryDiffEq", "ForwardDiff", "Tables"]
diff --git a/src/remake.jl b/src/remake.jl
index b84625fde..e4540cd68 100644
--- a/src/remake.jl
+++ b/src/remake.jl
@@ -567,6 +567,7 @@ end
 
 function fill_u0(prob, u0; defs = nothing, use_defaults = false)
     vsyms = variable_symbols(prob)
+    idx_to_vsym = anydict(variable_index(prob, sym) => sym for sym in vsyms)
     sym_to_idx = anydict()
     idx_to_sym = anydict()
     idx_to_val = anydict()
@@ -580,6 +581,8 @@ function fill_u0(prob, u0; defs = nothing, use_defaults = false)
             v = (v,)
         end
         for (kk, vv, ii) in zip(k, v, idx)
+            sym_to_idx[kk] = ii
+            kk = idx_to_vsym[ii]
             sym_to_idx[kk] = ii
             idx_to_sym[ii] = kk
             idx_to_val[ii] = vv
@@ -612,6 +615,7 @@ end
 
 function fill_p(prob, p; defs = nothing, use_defaults = false)
     psyms = parameter_symbols(prob)
+    idx_to_psym = anydict(parameter_index(prob, sym) => sym for sym in psyms)
     sym_to_idx = anydict()
     idx_to_sym = anydict()
     idx_to_val = anydict()
@@ -625,6 +629,8 @@ function fill_p(prob, p; defs = nothing, use_defaults = false)
             v = (v,)
         end
         for (kk, vv, ii) in zip(k, v, idx)
+            sym_to_idx[kk] = ii
+            kk = idx_to_psym[ii]
             sym_to_idx[kk] = ii
             idx_to_sym[ii] = kk
             idx_to_val[ii] = vv
@@ -707,6 +713,9 @@ function _updated_u0_p_symmap(prob, u0, ::Val{true}, p, ::Val{true}, t0)
     end
 
     varmap = merge(u0, p)
+    if is_time_dependent(prob)
+        varmap[only(independent_variable_symbols(prob))] = t0
+    end
     for (k, v) in u0
         u0[k] = symbolic_type(v) === NotSymbolic() ? v : symbolic_evaluate(v, varmap)
     end
diff --git a/test/downstream/modelingtoolkit_remake.jl b/test/downstream/modelingtoolkit_remake.jl
index 38d379ddc..d0df44658 100644
--- a/test/downstream/modelingtoolkit_remake.jl
+++ b/test/downstream/modelingtoolkit_remake.jl
@@ -229,3 +229,22 @@ end
     prob2 = remake(prob; u0 = [y => 3.0], p = Dict())
     @test prob2.ps[p] ≈ 4.0
 end
+
+@testset "u0 dependent on parameter given as Symbol" begin
+    @variables x(t)
+    @parameters p
+    @mtkbuild sys = ODESystem([D(x) ~ x * p], t)
+    prob = ODEProblem(sys, [x => 1.0], (0.0, 1.0), [p => 1.0])
+    @test prob.ps[p] ≈ 1.0
+    prob2 = remake(prob; u0 = [x => p], p = [:p => 2.0])
+    @test prob2[x] ≈ 2.0
+end
+
+@testset "remake dependent on indepvar" begin
+    @variables x(t)
+    @parameters p
+    @mtkbuild sys = ODESystem([D(x) ~ x * p], t)
+    prob = ODEProblem(sys, [x => 1.0], (0.0, 1.0), [p => 1.0])
+    prob2 = remake(prob; u0 = [x => t + 3.0])
+    @test prob2[x] ≈ 3.0
+end
diff --git a/test/downstream/solution_interface.jl b/test/downstream/solution_interface.jl
index 12e2c9402..cb6a07780 100644
--- a/test/downstream/solution_interface.jl
+++ b/test/downstream/solution_interface.jl
@@ -293,7 +293,7 @@ end
         prob = ODEProblem(sys, [x => 1.0, y => 1.0], (0.0, 5.0),
             [p => 0.5, q => 0.0, r => 1.0, s => 10.0, u => 4096.0])
         ss = SciMLBase.SavedSubsystem(sys, prob.p, [x, q, s, r])
-        @test SciMLBase.get_saved_state_idxs(ss) == [xidx]
+        @test SciMLBase.get_saved_state_idxs(ss) == [variable_index(sys, x)]
         sswf = SciMLBase.SavedSubsystemWithFallback(ss, sys)
         xidx = variable_index(sys, x)
         qidx = parameter_index(sys, q)
diff --git a/test/remake_tests.jl b/test/remake_tests.jl
index eff20c58e..dd6fdae5f 100644
--- a/test/remake_tests.jl
+++ b/test/remake_tests.jl
@@ -297,8 +297,36 @@ a = Remake_Test1(p = 1)
 @test @inferred remake(a, kwargs = (; a = 1)) == Remake_Test1(p = 1, a = 1)
 
 @testset "fill_u0 and fill_p ignore identical variables with different names" begin
-    sys = SymbolCache(Dict(:x => 1, :x2 => 1, :y => 2), Dict(:a => 1, :a2 => 1, :b => 2),
-        :t; defaults = Dict(:x => 1, :y => 2, :a => 3, :b => 4))
+    struct SCWrapper{S}
+        sc::S
+    end
+    SymbolicIndexingInterface.symbolic_container(s::SCWrapper) = s.sc
+    function SymbolicIndexingInterface.is_variable(s::SCWrapper, i::Symbol)
+        if i == :x2
+            return is_variable(s.sc, :x)
+        end
+        is_variable(s.sc, i)
+    end
+    function SymbolicIndexingInterface.variable_index(s::SCWrapper, i::Symbol)
+        if i == :x2
+            return variable_index(s.sc, :x)
+        end
+        variable_index(s.sc, i)
+    end
+    function SymbolicIndexingInterface.is_parameter(s::SCWrapper, i::Symbol)
+        if i == :a2
+            return is_parameter(s.sc, :a)
+        end
+        is_parameter(s.sc, i)
+    end
+    function SymbolicIndexingInterface.parameter_index(s::SCWrapper, i::Symbol)
+        if i == :a2
+            return parameter_index(s.sc, :a)
+        end
+        parameter_index(s.sc, i)
+    end
+    sys = SCWrapper(SymbolCache(Dict(:x => 1, :y => 2), Dict(:a => 1, :b => 2),
+        :t; defaults = Dict(:x => 1, :y => 2, :a => 3, :b => 4)))
     function foo(du, u, p, t)
         du .= u .* p
     end
@@ -306,17 +334,17 @@ a = Remake_Test1(p = 1)
     u0 = Dict(:x2 => 2)
     newu0 = SciMLBase.fill_u0(prob, u0; defs = default_values(sys))
     @test length(newu0) == 2
-    @test get(newu0, :x2, 0) == 2
+    @test get(newu0, :x, 0) == 2
     @test get(newu0, :y, 0) == 2.5
     p = Dict(:a2 => 3)
     newp = SciMLBase.fill_p(prob, p; defs = default_values(sys))
     @test length(newp) == 2
-    @test get(newp, :a2, 0) == 3
+    @test get(newp, :a, 0) == 3
     @test get(newp, :b, 0) == 4.5
 end
 
 @testset "value of `nothing` is ignored" begin
-    sys = SymbolCache(Dict(:x => 1, :x2 => 1, :y => 2), Dict(:a => 1, :a2 => 1, :b => 2),
+    sys = SymbolCache(Dict(:x => 1, :y => 2), Dict(:a => 1, :b => 2),
         :t; defaults = Dict(:x => 1, :y => 2, :a => 3, :b => 4))
     function foo(du, u, p, t)
         du .= u .* p