ggapp

GPU-accelerated Gaussian Process Prior

ggapp provides a fast, GPU-accelerated implementation of Gaussian process (GP) priors with a Matérn covariance, built for large spatial problems where forming a dense covariance matrix is infeasible. Rather than working with the covariance directly, it uses the SPDE representation of the Matérn field: a sample from a Matérn GP is obtained by repeatedly solving an elliptic (Laplacian-like) PDE driven by white noise. These solves are carried out on a structured grid with a geometric multigrid / Full Approximation Scheme (FAS) solver, with the heavy numerical kernels implemented as custom CUDA kernels and executed on the GPU through CuPy.

The result is a prior that supports the operations needed for Bayesian inference at scale:

• sample() — draw a realization from the Matérn prior.
• forward(z) — map a white-noise/whitened field to a sample from the prior (the square-root covariance applied to z).
• whiten(x) — the inverse map, transforming a field into the whitened space in which the prior is standard-normal.
• log_probability(x) — evaluate the (unnormalized) prior log-density.

These maps are exposed as differentiable PyTorch operations via the optional ggapp.torch module, so a ggapp prior can be dropped into a gradient-based inference or optimization pipeline.

The library is built on top of glide, which supplies the grid and field abstractions used throughout.

Requirements

ggapp runs on the GPU and requires:

• Python ≥ 3.10
• An NVIDIA GPU with a CUDA 12.x toolkit/driver (needed by cupy-cuda12x)

Dependencies

Core (always required)

Package	Constraint	Used for
cupy-cuda12x	>=12.0.0	GPU arrays, custom CUDA kernels (cupy, cupyx)
glide	—	Grid / field abstractions (glide.field)

Optional extras

Extra	Package(s)	Used for
torch	torch>=2.0	Differentiable PyTorch autograd integration (ggapp.torch)
examples	matplotlib>=3.5, scipy>=1.7	Running the scripts under examples/

These are declared in pyproject.toml and mirrored in requirements.txt (core) and requirements-optional.txt (extras).

Installation

Install the core package:

pip install .

Install with optional extras:

pip install ".[torch]"        # PyTorch integration
pip install ".[examples]"     # to run examples/
pip install ".[torch,examples]"

Or with the requirements files:

pip install -r requirements.txt                               # core only
pip install -r requirements.txt -r requirements-optional.txt  # everything

Quick start

from ggapp.model import MaternPrior

# A 2D Matern prior on a 256 x 256 grid with 5 multigrid levels.
prior = MaternPrior(n_levels=5, ny=256, nx=256, dx=1.0)

x = prior.sample()            # draw a realization from the prior
z = prior.whiten(x)           # map to the whitened (standard-normal) space
x_back = prior.forward(z)     # map back to a prior sample
logp = prior.log_probability(x)

See examples/toy/sample_gp.py for a runnable example (requires the examples extra).

License

See LICENSE.