Runnable examples

Every script below is the same file displayed in its guide. Install the exact package versions in the installation guide, download a script, and run it with Python.

Task	Script	Walkthrough
First activation derivative	first_derivative.py	Quickstart
Pure-Python coefficients	core_polynomial.py	Derivative identities
Trainable fourth derivative	high_order_torch.py	Residual tutorial
JAX residual gradient	high_order_jax.py	JAX walkthrough
Laplacian vs Hessian trace	deep_laplacian.py	Direct Laplacian
JAX Laplacian comparison	deep_laplacian_jax.py	JAX API
Mixed heat residual	mixed_heat.py	Heat residual
Trainable soft regions	soft_regions.py	Regional models
Functional Gauss–Newton	curvature.py	Curvature tutorial
Hard quantization and surrogate gradients	binary_torch.py, binary_jax.py	Hard decisions
Keras operator layer	keras_layer.py	Keras setup

Examples use small deterministic inputs and assert shape, numerical, or gradient properties. Benchmark speedups require the dedicated benchmark drivers and conditions; these learning scripts are not performance measurements.

The API reference also links upstream regression examples. Those tests may use fixtures and helpers from the full source checkout.

Complete scientific workflows

Explore the scientific ML notebook collection for beam bending, Poisson equations, trainable regions, and scientific calibration. Each download is executed against the pinned published packages.