Update for ModelingToolkit v11, OrdinaryDiffEq v7, DifferentialEquations v8

Bump compat for the breaking CompatHelper PRs:
- ModelingToolkit 10.10 -> 11 (main, test, docs)
- OrdinaryDiffEq 6 -> 7 (test)
- DifferentialEquations 7.6 -> 8 (docs)
- Replace ModelingToolkit `defaults` with `initial_conditions` in `deim`,
  storing numeric initial values for the reduced unknowns derived from
  the snapshot's first column. `defaults` was removed in MTK v11 and
  replaced by `bindings` (for symbolic expressions) and
  `initial_conditions` (for numeric values).
- Use `ModelingToolkit.bindings(sys)` semantics: keys must be whole array
  symbolics, not scalarized indices, hence the array-valued assignment.
- Switch the tutorial from `structural_simplify` (deprecated in MTK v10)
  to `mtkcompile`.
- Pass `missing_guess_value = ModelingToolkit.MissingGuessValue.Constant(0.0)`
  to `ODEProblem` for the MOL-discretized FitzHugh-Nagumo system in the
  test and docs to work around cyclic self-referencing guesses produced
  by `MethodOfLines` under MTK v11.

Closes/supersedes the breaking-major CompatHelper PRs:
#127, #128, #137 (ModelingToolkit -> 11), #146 (OrdinaryDiffEq -> 7),
#147 (DifferentialEquations -> 8).

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

Author: ChrisRackauckas

Project.toml

@@ -16,7 +16,7 @@ TSVD = "9449cd9e-2762-5aa3-a617-5413e99d722e"
 [compat]
 DocStringExtensions = "0.8, 0.9"
 LinearAlgebra = "1"
-ModelingToolkit = "10.10"
+ModelingToolkit = "11"
 PrecompileTools = "1"
 RandomizedLinAlg = "0.1"
 Setfield = "0.8, 1"

docs/Project.toml

@@ -9,10 +9,10 @@ ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 
 [compat]
-DifferentialEquations = "7.6"
+DifferentialEquations = "8"
 Documenter = "1"
 LaTeXStrings = "1.3"
 MethodOfLines = "0.11"
 ModelOrderReduction = "0.1"
-ModelingToolkit = "10"
+ModelingToolkit = "11"
 Plots = "1.40"

docs/src/tutorials/deim_FitzHugh-Nagumo.md

@@ -78,8 +78,9 @@ dxs = [x => dx]
 order = 2
 discretization = MOLFiniteDifference(dxs, t; approx_order = order)
 ode_sys, tspan = symbolic_discretize(pde_sys, discretization)
-simp_sys = structural_simplify(ode_sys)
-ode_prob = ODEProblem(simp_sys, nothing, tspan)
+simp_sys = mtkcompile(ode_sys)
+ode_prob = ODEProblem(simp_sys, nothing, tspan;
+    missing_guess_value = ModelingToolkit.MissingGuessValue.Constant(0.0))
 nothing # hide
 ```
 

src/deim.jl

@@ -176,13 +176,11 @@ function deim(
     )
     @set! sys.observed = new_sorted_observed
 
-    inv_dict = Dict(Symbolics.scalarize(ŷ .=> V' * dvs)) # reduced vars to original vars
-    @set! sys.defaults = merge(ModelingToolkit.defaults(sys), inv_dict)
-
-    # CRITICAL: Call complete() on the system before returning to ensure all subsystems,
-    # variables, and parameters are properly registered and namespaced. Without this,
-    # attempting to create an ODEProblem from the DEIM system will fail with errors about
-    # missing initial conditions for variables that should exist in the system.
-    # This is required due to changes in ModelingToolkit.jl's internal structure handling.
+    # Numeric initial conditions for the reduced unknowns from the snapshot's first column.
+    # The snapshot is assumed to start at t = tspan[1], matching the FOM initial state.
+    new_ics = copy(ModelingToolkit.get_initial_conditions(sys))
+    new_ics[Symbolics.unwrap(ŷ)] = V' * snapshot[:, 1]
+    @set! sys.initial_conditions = new_ics
+
     return complete(sys)
 end

test/Project.toml

@@ -11,6 +11,6 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 LinearAlgebra = "1"
 MethodOfLines = "0.11"
 Pkg = "1.10"
-ModelingToolkit = "10.10"
-OrdinaryDiffEq = "6"
+ModelingToolkit = "11"
+OrdinaryDiffEq = "7"
 SafeTestsets = "0.1"

test/deim.jl

@@ -38,7 +38,8 @@ order = 2
 discretization = MOLFiniteDifference(dxs, t; approx_order = order)
 ode_sys, tspan = symbolic_discretize(pde_sys, discretization)
 simp_sys = mtkcompile(ode_sys) # field substitutions is non-empty
-ode_prob = ODEProblem(simp_sys, nothing, tspan)
+ode_prob = ODEProblem(simp_sys, nothing, tspan;
+    missing_guess_value = ModelingToolkit.MissingGuessValue.Constant(0.0))
 sol = solve(ode_prob, Tsit5(), saveat = 1.0)
 
 snapshot_simpsys = Array(sol.original_sol)