Releases · JuliaMeshless/RadialBasisFunctions.jl

The operator type hierarchy now uses AbstractOperator{N} where N indicates the rank of the operator output. This replaces the previous flat hierarchy.
Custom operator now requires an explicit rank parameter: Custom{N}. Use Custom{0} for rank-preserving operators and Custom{1} for rank-increasing operators.

Features

Added RBFLayer as a LuxCore package extension for integrating RBF interpolation into Lux.jl neural networks

Bug Fixes

Reject ε=0 in Gaussian and IMQ constructors with a clear error
Fixed Lux guide and examples to use DifferentiationInterface with Mooncake backend for Julia 1.12 compatibility

Refactoring

Replaced OperatorArity trait with direct Tuple dispatch for cleaner operator weight handling
Constrained operator method signatures to AbstractOperator for type safety

Documentation

Added docstring for AbstractOperator{N}
Updated references after operator type hierarchy refactor
Added Julia best practices section to CLAUDE.md

CI & Maintenance

Fixed downgrade CI failures across Julia 1.10–1.12
Updated dependency compat bounds for docs and benchmarks

Merged pull requests:

chore(deps): bump actions/upload-artifact from 6 to 7 (#98) (@dependabot[bot])
chore(deps): bump the all-julia-packages group across 1 directory with 9 updates (#108) (@dependabot[bot])
feat: RBFLayer for Lux.jl, fix Gaussian/IMQ ε validation (#109) (@kylebeggs)

Closed issues:

Radial basis function networks? (#45)
fix dev documentation build (#67)

Contributors

kylebeggs and dependabot

Assets 2

20 Feb 22:27

github-actions

v0.3.0

3a5beb6

v0.3.0

RadialBasisFunctions v0.3.0

Diff since v0.2.7

Breaking Changes

Gradient type removed — gradient(...) is now a convenience alias for jacobian(...). Code that used Gradient as a type directly will break.
Basis operator closures replaced with functor structs — ∂, ∇, ∂², ∇², D, D² are now callable structs instead of closure-returning functions. The public API (∂(basis, dim), etc.) is unchanged, but code dispatching on closure types will need updating.
RadialBasisOperator gained a device type parameter — struct now has 7 type parameters (was 6). Code pattern-matching on the full parametric type may need updating.

New Features

Automatic Differentiation Support (Enzyme.jl & Mooncake.jl)

Native reverse-mode AD via package extensions (auto-activated when Enzyme or Mooncake is loaded)
Enzyme extension — EnzymeRules (augmented_primal + reverse) for operator application, _build_weights, and basis evaluation
Mooncake extension — rrule!! with @is_primitive for operator application, _build_weights, Interpolator construction, and basis evaluation
Shared backward pass (src/solve/backward.jl) using the implicit function theorem to differentiate through the stencil linear solve
Differentiable w.r.t. data point locations and basis shape parameter ε
Analytic second derivatives for all PHS orders, Gaussian, and IMQ (needed for chain rule through RHS assembly)
Shape parameter derivatives (∂φ/∂ε, ∂∇²φ/∂ε, ∂∂φ/∂ε) for Gaussian and IMQ bases
BLAS-optimized backward pass using mul! rank-1 updates
Compatible with DifferentiationInterface.jl for a unified AD interface

Jacobian Operator

New Jacobian operator replaces the old Gradient type
Generalizes beyond scalar fields: scalar input → (N_eval × D) gradient; vector input → (N_eval × D × D) Jacobian; higher-rank tensor support
gradient(...) is preserved as a convenience alias

Hessian Basis Functor

New H (Hessian) functor for all basis types (PHS 1/3/5/7, Gaussian, IMQ)
Returns SMatrix{N,N,T} for second-derivative matrix of basis functions
Used internally by Hermite dispatch for optimized second-derivative computation

GPU Improvements

device keyword on all operator constructors — auto-detects backend via KernelAbstractions.get_backend(data) or explicit override (e.g., device=CUDABackend())
Adapt.jl support — Adapt.adapt_structure for RadialBasisOperator and Interpolator, enabling adapt(CUDABackend(), op)
GPU array types preserved in operator algebra (+/-)
VectorValuedOperator evaluation uses mul! with views to eliminate temporaries
Interpolator batch evaluation accepts AbstractVector{<:AbstractVector} (not just Vector)
show methods use eltype() instead of typeof(first()) for GPU compatibility

Unified Keyword-Based Constructor API

Primary RadialBasisOperator constructor rewritten with keyword arguments:

RadialBasisOperator(ℒ, data;
    eval_points=data, basis=PHS(3; poly_deg=2),
    k=autoselect_k(data, basis), adjl=...,
    hermite=nothing, device=get_backend(data))

hermite keyword accepts a NamedTuple (is_boundary=..., bc=..., normals=...) replacing old positional arguments
All operator constructors (laplacian, partial, gradient, jacobian, directional, custom, regrid) forward kw... to unified constructor

Refactoring

Basis Functions: Closures to Functors

All differential operator factories replaced with typed callable structs (∂{B}, ∇{B}, ∂²{B}, ∇²{B}, D{B,V}, D²{B,V1,V2}, H{B})
Enables multiple dispatch in AD rules and across the codebase
PHS normal dispatch refactored to use 3-argument call instead of Union{AbstractVector,Nothing}

Solve System Reorganization

stencil_math.jl → assembly.jl (pure math: collocation matrix, RHS, stencil assembly)
kernel_exec.jl → execution.jl (memory allocation, kernel launching, batch processing)
New BasisOperators struct packages basis + gradient + Hessian functors, computed once per stencil
6 new files for AD support (ad_shared.jl, backward.jl, backward_cache.jl, forward_cache.jl, operator_second_derivatives.jl, shape_parameter_derivatives.jl)

Performance

Pre-allocated λ buffer reused across stencils in solve loop (fewer allocations)
view(data, neighbors) instead of [data[i] for i in neighbors] per stencil
dot() instead of intermediate allocations in polynomial evaluation
mul! with views in VectorValuedOperator evaluation (zero-allocation GPU-friendly)

Testing

Comprehensive AD test suite (test/extensions/autodiff_di.jl) testing Laplacian, Gradient, Partial, Interpolator (construction + evaluation), basis functions, shape parameter differentiation, and 3D operators against finite differences
All rand/randn calls seeded with MersenneTwister for deterministic CI
New test files for Jacobian operator, device keyword, and individual extension tests
Enzyme tests skipped on Julia 1.12+ (VERSION < v"1.12")

Documentation

Switched to DocumenterVitepress.jl frontend
New autodiff guide (docs/src/guides/autodiff.md) with runnable examples using DI.AutoMooncake
New quick reference page (docs/src/guides/quickref.md)
Restructured navigation with Guides and Reference sections
Refreshed landing page and README

Infrastructure

Formatter switched from JuliaFormatter.jl to Runic.jl
New dependencies: Adapt.jl, StaticArrays.jl (direct); Enzyme.jl, EnzymeCore.jl, Mooncake.jl (weak deps)
CI action bumps (checkout v6, upload-artifact v6, etc.)
ChainRulesCore dependency removed

Merged pull requests:

Refactor polynomial for Hermite (#60) (@kylebeggs)
Jacobian operator and autodiff support (#61) (@kylebeggs)
refactor(basis): replace operator closures with functor types (#64) (@kylebeggs)
Feature/runic formatter (#66) (@kylebeggs)
docs: enhance LLM discoverability and developer documentation (#68) (@kylebeggs)
chore(deps): bump Mooncake compat to 0.5 (#72) (@kylebeggs)
add native Enzyme rules and enhanced autodiff support (#76) (@kylebeggs)
Bump julia-actions/julia-downgrade-compat from 1 to 2 (#77) (@dependabot[bot])
Bump peter-evans/create-or-update-comment from 4 to 5 (#78) (@dependabot[bot])
Bump peter-evans/find-comment from 3 to 4 (#79) (@dependabot[bot])
Bump actions/upload-artifact from 4 to 6 (#80) (@dependabot[bot])
Bump actions/checkout from 4 to 6 (#81) (@dependabot[bot])
feat(ad): replace CRC extension with native Enzyme and Mooncake rules (#83) (@kylebeggs)
perf(solve): reduce memory allocations in solve system hot paths (#85) (@kylebeggs)
docs refresh (#87) (@kylebeggs)
GPU updates (#89) (@kylebeggs)

Closed issues:

improve the code for boundary conditions (#47)
improve handling of polynomial terms (#48)
Refactor RBF operators to use functor pattern for proper multiple dispatch (#62)
Removal of repeated code in src/operators (#63)
EnzymeRules? (#71)
perf: optimize memory allocations in solve system hot paths (#73)
feat(enzyme): add _build_weights support for IMQ and Gaussian basis functions (#74)

Contributors

kylebeggs and dependabot

Assets 2

18 Nov 02:01

github-actions

v0.2.6

62f119e

v0.2.6

RadialBasisFunctions v0.2.6

Diff since v0.2.5

✨ New Features

Hermite Interpolation with Boundary Conditions

Added comprehensive support for Hermite interpolation, enabling derivative boundary conditions alongside
function values for PDE solving:

Dirichlet Boundary Conditions: Specify function values at boundaries
Neumann Boundary Conditions: Specify derivative values at boundaries
Robin Boundary Conditions: Specify linear combinations of function and derivative values
Mixed Boundary Conditions: Combine different boundary condition types in the same problem
Works seamlessly with all RBF operators (Gradient, Laplacian, Partial, Directional, Custom)

GPU/CPU Parallelization with KernelAbstractions.jl

Migrated to KernelAbstractions.jl for improved parallel execution:

Unified GPU and CPU computation backends
Improved performance for weight computation
Better memory management with stencil weight preallocation

🐛 Bug Fixes

Fixed bug in Hermite weight computation (solve_hermite.jl)
Fixed polyharmonic spline derivative calculation bug
Fixed interpolation weights to correctly include last data point in linear system solve
Corrected polyharmonic spline keyword constructors

Merged pull requests:

Refactor of operator typing (#37) (@kylebeggs)
Update README.md (#38) (@kylebeggs)
Hermite conditions (#40) (@Davide-Miotti)
Use KernelAbstractions.jl (#41) (@kylebeggs)
Add Claude Code GitHub Workflow (#42) (@kylebeggs)
Hermite kyle davide (#44) (@Davide-Miotti)
Include last data point in linear system solve for interpolating weights (#46) (@cgeoga)
Hermite refactor (#53) (@kylebeggs)
Addition of Hermite method (#54) (@kylebeggs)
add description of Hermite approach (#56) (@Davide-Miotti)
add multithread CI and update actions (#58) (@kylebeggs)