Fix Basis compatibility with ODEProblem (#552)

This commit fixes the issue where using a Basis object obtained from DMD
or SINDy as the ODE function in ODEProblem would throw an error about
the 'observed' field not existing.

Changes:
- Added ModelingToolkit interface methods for Basis in new file
  src/basis/modelingtoolkit_interface.jl
- Implemented required AbstractSystem interface methods: equations, unknowns,
  parameters, get_observed, get_iv, nameof
- Override getproperty to properly handle :observed field access
- Override show method to fix display error related to namespacing flag
- Added conditional definitions for namespacing-related methods to maintain
  compatibility across ModelingToolkit versions

Fixes #552

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <[email protected]>

Author: ChrisRackauckas

src/DataDrivenDiffEq.jl

@@ -96,6 +96,7 @@ struct ZeroDataDrivenAlgorithm <: AbstractDataDrivenAlgorithm end
 include("./basis/build_function.jl")
 include("./basis/utils.jl")
 include("./basis/type.jl")
+include("./basis/modelingtoolkit_interface.jl")
 export Basis
 export jacobian, dynamics
 export implicit_variables, states, controls

src/basis/modelingtoolkit_interface.jl

@@ -0,0 +1,62 @@
+# ModelingToolkit interface methods for Basis
+
+import ModelingToolkit: equations, unknowns, parameters, get_observed, get_iv, nameof
+
+# Equations
+function ModelingToolkit.equations(b::AbstractBasis)
+    return getfield(b, :eqs)
+end
+
+# Unknowns (states)
+function ModelingToolkit.unknowns(b::AbstractBasis)
+    return states(b)
+end
+
+# Parameters
+function ModelingToolkit.parameters(b::AbstractBasis)
+    return getfield(b, :ps)
+end
+
+# Observed
+function ModelingToolkit.get_observed(b::AbstractBasis)
+    return getfield(b, :observed)
+end
+
+# Independent variable
+function ModelingToolkit.get_iv(b::AbstractBasis)
+    return getfield(b, :iv)
+end
+
+# Name
+function ModelingToolkit.nameof(b::AbstractBasis)
+    return getfield(b, :name)
+end
+
+# Define has_namespacing to indicate that Basis doesn't support namespacing
+if isdefined(ModelingToolkit, :has_namespacing)
+    function ModelingToolkit.has_namespacing(::AbstractBasis)
+        return false
+    end
+end
+
+# Define namespace_expression if it exists
+if isdefined(ModelingToolkit, :namespace_expression)
+    function ModelingToolkit.namespace_expression(b::AbstractBasis)
+        return false  # Basis doesn't support namespacing
+    end
+end
+
+# Override getproperty to handle :observed specially
+function Base.getproperty(b::AbstractBasis, name::Symbol)
+    if name === :observed
+        return get_observed(b)
+    else
+        # Fall back to getfield for direct field access
+        return getfield(b, name)
+    end
+end
+
+# Override show to avoid ModelingToolkit's display method that needs namespacing
+function Base.show(io::IO, ::MIME"text/plain", b::AbstractBasis)
+    Base.print(io, b)
+end