spde

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.

Bayesian inference on spatial and spatiotemporal data, faster than you can say "Cholesky!"

Code and data from the "Spatial and Spatio-temporal Bayesian Models with R-INLA" book

Stochastic PDE solvers (SPDE) built on top of exponax: Exponential Euler-Maruyama stepper for the stochastic Allen-Cahn equation with additive/multiplicative Q-Wiener noise, tamed nonlinearities, ensemble utilities, Richardson extrapolation, and a Strang-split hybrid SSA scaffold.

An introductory course to the INLA-software

Large-scale prior fields based on the SPDE approach to Matérn fields

Bibliograph bank for stochastic PDE and related fields

A four-dimensional inhomogeneous, anisotropic Gaussian random field generator.

Lean 4 companion (partial formalization) to the second moment of the Stratonovich hyperbolic Anderson model: finite, algebraic and scalar steps checked by Lean, analytic inputs as explicit hypotheses; correspondence reviewed by AI, not by a human.

Applied Spatial Data Analysis in geoscience

Large-Scale Prior Fields via SPDEs

Elevational variation in tropical trees analysis

Slide deck: A class of d-dimensional directed polymers in a Gaussian environment (CUHK-Shenzhen, May 6 2026)

Julia scripts associated with "A White Noise Approach to Evolutionary Ecology" by Week et. al. (2020) for simulating branching Brownian motions and other measure-valued branching processes, approximating their diffusion limits, solving associated SPDE and solving SDE corresponding to an eco-evolutionary model of a competitive community.

Constrained Delaunay triangulation meshes and FEM matrix assembly for spatial SPDE models

Transport-SPDE covariance research toolkit with PSD-constrained estimation, observation diagnostics, and reproducible numerical benchmarks.

Chebyshev exponential-integrator solver for stochastic PDEs on bounded domains

Numerics for white noise and the stochastic heat equation on the torus. Python API, C++/pybind11 hot kernels, analytic Monte Carlo tests.

Compare two codebases quickly in the browser, showing added, deleted, modified, and moved files with a fast, non-blocking diff engine.

Code for proceeding paper in FIMH2019