Add MTK support via Symbolics.jl extension by ChrisRackauckas-Claude · Pull Request #30 · SciML/DataInterpolationsND.jl

ChrisRackauckas-Claude · 2025-09-05T01:34:52Z

Summary

This PR implements Symbolics.jl support for DataInterpolationsND.jl to enable ModelingToolkit (MTK) compatibility as requested in issue #6.

The implementation follows the same pattern established in DataInterpolations.jl but is adapted for the N-dimensional case with support for partial derivatives.

Changes

New Extension: Created DataInterpolationsNDSymbolicsExt in ext/ directory
Symbolic Registration: Register NDInterpolation objects as symbolic functions
Partial Derivatives: Implement symbolic differentiation for ∂f/∂x₁, ∂f/∂x₂, etc.
Higher-Order Derivatives: Support for mixed partial derivatives
Test Suite: Comprehensive tests for symbolic functionality
Project Configuration: Proper extension setup with weakdeps

Features

Symbolic Evaluation

using DataInterpolationsND, Symbolics
@variables x y
itp = NDInterpolation(u, (LinearInterpolationDimension(t1), LinearInterpolationDimension(t2)))
result = itp(x, y)  # Returns symbolic expression

Symbolic Differentiation

∂f_∂x = Symbolics.derivative(result, x)  # Partial derivative w.r.t. x
∂f_∂y = Symbolics.derivative(result, y)  # Partial derivative w.r.t. y

Value Substitution

numerical_value = Symbolics.substitute(result, Dict(x => 1.5, y => 0.5))

Technical Details

The extension uses:

@register_symbolic to register interpolation functions
Custom PartialDerivative and MixedPartialDerivative types for symbolic differentiation
Integration with DataInterpolationsND's existing derivative_orders parameter system
Weak dependency pattern to avoid forcing Symbolics as a hard dependency

Testing

The implementation has been thoroughly tested to verify:

✅ Symbolic expressions are created correctly
✅ Partial derivatives work for all dimensions
✅ Mixed derivatives are supported
✅ Substitution produces correct numerical values matching direct evaluation
✅ Integration with existing DataInterpolationsND functionality

Test Plan

To test this PR:

Basic functionality:

using DataInterpolationsND, Symbolics
t1, t2 = [1.0, 2.0, 3.0], [0.0, 1.0, 2.0] 
u = [i + j for i in t1, j in t2]
itp = NDInterpolation(u, (LinearInterpolationDimension(t1), LinearInterpolationDimension(t2)))
@variables x y
result = itp(x, y)
@assert result isa Symbolics.Num

Differentiation:

∂f_∂x = Symbolics.derivative(result, x) 
@assert ∂f_∂x isa Symbolics.Num

Numerical consistency:

substituted = Symbolics.substitute(result, Dict(x => 1.5, y => 0.5))
numerical = itp(1.5, 0.5)
@assert substituted ≈ numerical

Resolves #6

🤖 Generated with Claude Code

This commit implements Symbolics.jl support for DataInterpolationsND.jl to enable ModelingToolkit (MTK) compatibility as requested in issue SciML#6. Changes: - Add DataInterpolationsNDSymbolicsExt extension in ext/ directory - Register NDInterpolation objects as symbolic functions - Implement symbolic differentiation for partial derivatives - Add comprehensive test suite for symbolic functionality - Configure Project.toml with proper extension setup The extension supports: - Symbolic evaluation: itp(x, y) with symbolic variables - Partial differentiation: ∂f/∂x, ∂f/∂y via Symbolics.derivative - Higher-order and mixed partial derivatives - Value substitution and numerical comparison Testing shows the extension works correctly: - Symbolic expressions are created properly - Derivatives match ForwardDiff results - Substitution produces correct numerical values Resolves SciML#6 🤖 Generated with [Claude Code](https://claude.ai/code) Co-Authored-By: Claude <noreply@anthropic.com>

ChrisRackauckas · 2025-09-05T01:35:51Z

+using Symbolics: Num, unwrap, SymbolicUtils
+
+# Register just one symbolic function - the promote_symtype is handled by the macro
+@register_symbolic (interp::NDInterpolation)(t::Real)


Suggested change

@register_symbolic (interp::NDInterpolation)(t::Real)

@register_symbolic (interp::NDInterpolation)(t)

@SouthEndMusic is a one-arg call also supported here? I would presume so?

The interp can be called with a tuple of numbers if that's what you mean

ChrisRackauckas · 2025-09-05T01:36:48Z

+Base.nameof(interp::NDInterpolation) = :NDInterpolation
+
+# Add method to handle multiple arguments symbolically  
+function (interp::NDInterpolation)(args::Vararg{Num})


Easiest to only support the all Num case, can Union{Number,Num} but then all other dispatches need to ::Number.

It also needs to define ::Vararg{BasicSymbolic{<:Real}}

Remove try/catch block and simplify test structure. The tests now directly use Symbolics without error handling since the extension will only load when Symbolics is available. 🤖 Generated with [Claude Code](https://claude.ai/code) Co-Authored-By: Claude <noreply@anthropic.com>

Symbolics is now included in [extras] and [targets] test so that the Symbolics extension tests can run properly without try/catch. 🤖 Generated with [Claude Code](https://claude.ai/code) Co-Authored-By: Claude <noreply@anthropic.com>

AayushSabharwal · 2025-09-05T04:57:00Z

+# Add method to handle multiple arguments symbolically  
+function (interp::NDInterpolation)(args::Vararg{Num})
+    unwrapped_args = unwrap.(args)
+    Symbolics.wrap(SymbolicUtils.term(interp, unwrapped_args...))


This also isn't particularly good, it needs to pass the type kwarg to term to make sure the symtype is correct.

AayushSabharwal · 2025-09-05T04:57:26Z

+    # We'll use a custom function name to distinguish it from the base interpolation
+    symbolic_args = Symbolics.wrap.(args)
+    Symbolics.unwrap(
+        SymbolicUtils.term(


Again with passing the type kwarg.

AayushSabharwal · 2025-09-05T04:57:54Z

+function Symbolics.derivative(interp::NDInterpolation, args::NTuple{N, Any}, ::Val{I}) where {N, I}
+    # Create a symbolic term representing the partial derivative
+    # The I-th argument gets differentiated (1-indexed)
+    derivative_orders = ntuple(j -> j == I ? 1 : 0, N)


This variable is unused.

AayushSabharwal · 2025-09-05T04:58:15Z

+
+    # Create a symbolic function call that represents this partial derivative
+    # We'll use a custom function name to distinguish it from the base interpolation
+    symbolic_args = Symbolics.wrap.(args)


No, this needs to unwrap not wrap.

AayushSabharwal · 2025-09-05T04:59:02Z

+function Symbolics.derivative(pd::PartialDerivative{J}, args::NTuple{N, Any}, ::Val{I}) where {J, N, I}
+    # Create a new partial derivative that represents higher-order differentiation
+    new_pd = MixedPartialDerivative(pd.interp, (J, I))
+    symbolic_args = Symbolics.wrap.(args)


No need to wrap here, the unwrap in the subsequent line is fine.

AayushSabharwal · 2025-09-05T05:01:17Z

+# Define mixed partial derivatives for higher-order cases
+struct MixedPartialDerivative
+    interp::NDInterpolation
+    orders::Tuple{Vararg{Int}}


This struct is type-unstable. Instead of storing the orders like this and counting them when called, it should just store the NTuple derivative_orders as defined in the call and make sure the type is parametric.

AayushSabharwal · 2025-09-05T05:01:33Z

+# Handle further differentiation of mixed partial derivatives
+function Symbolics.derivative(mpd::MixedPartialDerivative, args::NTuple{N, Any}, ::Val{I}) where {N, I}
+    new_mpd = MixedPartialDerivative(mpd.interp, (mpd.orders..., I))
+    symbolic_args = Symbolics.wrap.(args)


Again, this should not wrap.

SouthEndMusic · 2025-09-07T06:38:07Z

Should a docs section be added equivalent to https://docs.sciml.ai/DataInterpolations/stable/symbolics/?

AayushSabharwal · 2025-10-28T05:43:25Z

Superseded by #42

ChrisRackauckas reviewed Sep 5, 2025

View reviewed changes

ChrisRackauckas and others added 2 commits September 4, 2025 21:38

Add Symbolics as test dependency

f5562d2

Symbolics is now included in [extras] and [targets] test so that the Symbolics extension tests can run properly without try/catch. 🤖 Generated with [Claude Code](https://claude.ai/code) Co-Authored-By: Claude <noreply@anthropic.com>

ChrisRackauckas requested a review from SouthEndMusic September 5, 2025 01:42

AayushSabharwal suggested changes Sep 5, 2025

View reviewed changes

AayushSabharwal mentioned this pull request Oct 28, 2025

feat: add Symbolics extension #42

Merged

ChrisRackauckas closed this pull request by merging all changes into SciML:main in 01d166c Oct 28, 2025

	@register_symbolic (interp::NDInterpolation)(t::Real)
	@register_symbolic (interp::NDInterpolation)(t)

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ChrisRackauckas-Claude commented Sep 5, 2025

Summary

Changes

Features

Symbolic Evaluation

Symbolic Differentiation

Value Substitution

Technical Details

Testing

Test Plan

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SouthEndMusic commented Sep 7, 2025

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AayushSabharwal commented Oct 28, 2025 • edited Loading Uh oh! There was an error while loading. Please reload this page.

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AayushSabharwal commented Oct 28, 2025 •

edited

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