wias — Weak Identification of Analytic Systems

wias is a Python library for data-driven identification of analytic systems in weak form based on the paper: A zero-one law for one-shot system identification by Nicolas Boullé, Diana Halikias, Samuel E. Otto, and Alex Townsend.

Features

• Weak-form assembly for first- and second-order ODE systems
• Sinusoidal test-function basis construction
• Column-pivoted QR solver (CPQR_solver) for coefficient recovery
• PDE support via optional Firedrake integration for finite-element weak-form assembly
• Recovery of linearly-parametrized matrix families

Examples

Lorenz attractor

The identified model accurately reconstructs the chaotic Lorenz trajectory from noisy data.

Duffing oscillator

The phase portrait and time series of the identified Duffing oscillator match the ground truth closely over long integration times.

More examples are available in the examples/ folder, including Allen–Cahn, Navier–Stokes, and Hankel/circulant matrix problems.

Level-set for algebraic equations

Compute zero level set of a parameter-to-recovery map to identify inputs that lie in the degenerate set and do not allow recovery of the underlying system.

Installation

pip install wias

or

git clone https://github.com/NBoulle/wias
cd wias
pip install .

Optional: Firedrake (PDE support)

PDE identification via wias.weak_assembly requires Firedrake. Follow the official installation instructions at https://www.firedrakeproject.org/install.html. Once installed, assemble_weak_library_rows becomes available automatically.

Citing WIAS

If you use wias in your research, please cite the following paper:

@article{boulle2026zero,
  title={A zero-one law for one-shot system identification},
  author={Boull\'e, Nicolas and Halikias, Diana and Otto, Samuel E. and Townsend, Alex},
  journal={arXiv preprint arXiv:2607.15832},
  year={2026}
}