NumSDE

Numerical methods for stochastic differential equations, for teaching and research.

NumSDE provides readable, thoroughly tested reference implementations of numerical schemes for Itô stochastic differential equations

$$\mathrm{d}X(t) = f(t, X(t))\,\mathrm{d}t + g(t, X(t))\,\mathrm{d}W(t), \qquad X(t) \in \mathbb{R}^d,\; W(t) \in \mathbb{R}^m,$$

together with tools for empirical strong and weak convergence studies and a benchmark suite for comparing new schemes with established ones.

Status: early development (milestone M0, foundations). The API is not usable yet. See the architecture and roadmap.

Goals

• Readable code: each scheme's step() mirrors its textbook update rule.
• Verified: unit, property-based, statistical and regression tests; every scheme's empirical convergence order is checked against theory.
• Didactic documentation: a theory page for every scheme and executable tutorials.
• Vectorized: many paths are simulated at once; NumPy first, PyTorch (GPU) through the same code via the Python Array API standard.

Installation

Once released:

pip install numsde              # core: NumPy and array-api-compat
pip install "numsde[symbolic]"  # + SymPy for symbolic derivatives
pip install "numsde[plot]"      # + matplotlib
pip install "numsde[torch]"     # + PyTorch backend
pip install "numsde[all]"

For development, see CONTRIBUTING.md.

Citing NumSDE

If you use NumSDE in your research, please cite it using the metadata in CITATION.cff.

License

NumSDE is distributed under the BSD 3-Clause License.