Gaussian Random Field (GRF)

Gaussian Random Field generator with efficient score computation via FFT.

Adapted from Devito's Darcy flow example.

Installation

pip install -e .

With visualization support:

pip install -e ".[viz]"

Usage

import numpy as np
from grf_with_score import GaussianRandomField

# Create a 2D GRF with values mostly in [0.01, 0.5]
grf = GaussianRandomField(dim=2, size=128, bounds=(0.01, 0.5))

# Generate samples
samples = grf.sample(10)  # shape: (10, 128, 128)

# Compute score (gradient of log probability)
score = grf.score(samples[0])

# Compute log probability
log_p = grf.log_prob(samples[0])

Parameters

Parameter	Type	Default	Description
dim	int	-	Dimensionality (only 2D supported)
size	int	-	Grid size in each dimension
alpha	float	3	Power exponent controlling smoothness
tau	float	5	Scale parameter for correlation length
sigma	float	None	Internal scaling (auto-computed if None)
boundary	str	"periodic"	Boundary conditions
bounds	tuple	None	(low, high) bounds for output scaling

Methods

• sample(N) - Generate N samples from the GRF
• score(M) - Compute ∇_M log p(M)
• log_prob(M) - Compute log p(M)

Examples

GRF Samples

Score Field

Gradient Descent

License

MIT