Remove ModelingToolkit dependency from ODEProblemLibrary for faster compilation

[ChrisRackauckas]

Summary

This PR removes the ModelingToolkit dependency from ODEProblemLibrary by rewriting all ModelingToolkit-dependent example problems to use direct ODE function definitions instead of symbolic computation. This significantly improves compilation speed and eliminates circular dependency issues.

Motivation

• Circular dependency issue: ModelingToolkit → DiffEqCallbacks → ODEProblemLibrary → ModelingToolkit was causing precompilation failures
• Slow compilation: Symbolic computation overhead was making package loading slow
• Dependency bloat: ModelingToolkit added significant dependency footprint for simple ODE examples

Changes Made

Dependencies

• Removed ModelingToolkit from [deps] in Project.toml
• Removed Latexify dependency (was only used for ModelingToolkit documentation)
• Removed RuntimeGeneratedFunctions dependency (not needed for direct ODE functions)

Rewritten Problems

ode_simple_nonlinear_prob.jl:

• Van der Pol equations (prob_ode_vanderpol, prob_ode_vanderpol_stiff)
• ROBER biochemical reactions (prob_ode_rober)
• Rigid body equations (prob_ode_rigidbody)
• Hires problem (prob_ode_hires)
• Orego problem (prob_ode_orego)

strange_attractors.jl:

• Thomas cyclically symmetric attractor (prob_ode_thomas)
• Lorenz equations (prob_ode_lorenz)
• Aizawa equations (prob_ode_aizawa)
• Dadras equations (prob_ode_dadras)
• Chen equations (prob_ode_chen)
• Rössler equations (prob_ode_rossler)
• Rabinovich-Fabrikant equations (prob_ode_rabinovich_fabrikant)
• Sprott equations (prob_ode_sprott)
• Hindmarsh-Rose equations (prob_ode_hindmarsh_rose)

Benefits

✅ Faster compilation: No symbolic computation overhead
✅ Eliminated circular dependencies: Resolves ModelingToolkit circular dependency
✅ Reduced dependency footprint: Fewer dependencies to install and manage
✅ Better test reliability: No more precompilation failures
✅ Maintained API compatibility: All exports remain the same
✅ Preserved accuracy: Same mathematical formulations, initial conditions, and parameters

Testing

• All Aqua.jl quality assurance tests pass
• All rewritten problems maintain correct dimensions, initial conditions, and parameters
• ODE functions are callable and produce finite derivatives
• Backward compatibility maintained with existing code
• No breaking changes to the public API

Example: Van der Pol Before/After

Before (ModelingToolkit):

@parameters μ
@variables x(t) y(t)
eqs = [D(y) ~ μ * ((1 - x^2) * y - x), D(x) ~ y]
van = System(eqs, t; name = :van_der_pol) |> mtkcompile
prob_ode_vanderpol = ODEProblem(van, [y => 0, x => sqrt(3), μ => 1.0], (0.0, 1.0))

After (Direct ODE):

function vanderpol(du, u, p, t)
    x, y = u
    μ = p[1]
    du[1] = y
    du[2] = μ * ((1 - x^2) * y - x)
end
prob_ode_vanderpol = ODEProblem(vanderpol, [sqrt(3), 0.0], (0.0, 1.0), [1.0])

Test Plan

• All Aqua.jl tests pass
• Package loads without ModelingToolkit dependency
• All problem exports are available
• ODE functions produce correct derivatives
• Initial conditions and parameters are preserved
• No circular dependency warnings

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