INLASPDE.jl

INLASPDE.jl

SPDE–Matérn Gaussian random fields on triangulated meshes, for use as AbstractLatentComponent in the LatentGaussianModels.jl framework.

Implements the stochastic partial differential equation approach of Lindgren, Rue & Lindström (2011), which links Matérn Gaussian fields to sparse Gaussian Markov random fields via finite-element projections on a mesh. This is the native-Julia equivalent of R-INLA's SPDE + fmesher functionality.

Status

v0.1.0-rc1. Shipped:

• SPDE2 — α = 2 SPDE-Matérn AbstractLatentComponent.
• PCMatern — joint PC prior on (range, σ).
• inla_mesh_2d — DT.jl-native constrained-Delaunay mesh generator matching R-INLA's inla.mesh.2d on convex domains.
• MeshProjector — A-matrix mapping mesh vertices to observation points, exposed as a SciMLOperators.AbstractSciMLOperator.

Validated against R-INLA on the Meuse zinc dataset (see test/oracle/test_meuse_spde.jl). Higher-α and fractional SPDE (Bolin-Kirchner 2020) are deferred to v0.3.

Quick example — Meuse zinc

The actual API exercised by the Meuse oracle test:

using INLASPDE, LatentGaussianModels, SparseArrays

# `points :: Matrix{Float64}` (n_v × 2) — mesh vertex coordinates
# `tv     :: Matrix{Int}`     (n_t × 3) — triangle index list (1-based)
# `A_field :: SparseMatrixCSC` (n_obs × n_v) — projector to obs locations

spde = SPDE2(points, tv; α = 2,
    pc = PCMatern(
        range_U = 0.5, range_α = 0.5,   # P(range < 0.5) = 0.5
        sigma_U = 1.0, sigma_α = 0.5,   # P(σ > 1.0)     = 0.5
    ))

intercept = Intercept(prec = 1.0e-3)
beta_dist = FixedEffects(1; prec = 1.0e-3)

# Latent layout: x = [α, β_dist, u(field)]
A = hcat(ones(n_obs, 1),
        reshape(dist_cov, n_obs, 1),
        A_field)

like  = GaussianLikelihood(hyperprior = PCPrecision(1.0, 0.01))
model = LatentGaussianModel(like, (intercept, beta_dist, spde), A)

res = inla(model, y)

For mesh generation from a polygon, use:

mesh = inla_mesh_2d(boundary; max_edge = (0.05, 0.2), cutoff = 0.02)
points, tv = mesh.loc, mesh.tv

Installation

Registered on a personal Julia registry at haavardhvarnes/JuliaRegistry — add it once, then Pkg.add as usual:

using Pkg
Pkg.Registry.add(RegistrySpec(url = "https://github.com/haavardhvarnes/JuliaRegistry"))
Pkg.add("INLASPDE")

See also

• GMRFs.jl — sparse precision substrate.
• LatentGaussianModels.jl — LGM framework that consumes SPDE components.
• INLASPDERasters.jl — raster ↔ SPDE glue (planning).
• Meshes.jl — mesh representation.
• DelaunayTriangulation.jl — the constrained-Delaunay engine under the hood.