Examples

Each example is a script you run from a repository checkout. Install the example dependencies once:

uv sync --extra examples

Example	What it teaches	Run it
Harmonic oscillator	HybridModel fit, predict and simulate on a one-Parameter problem with a known answer. Start here.	uv run python examples/pendulum/train_harmonic.py --no-plot
Crystallisation	Irregular multi-channel data, two bounded neural rates, and a population-balance ODE.	uv run python examples/crystallisation/train_kinetic.py
Hybrid ODE	One network above the solver and one inside the vector field, log warps, and the saturation penalty.	uv run python examples/hybrid_ode/train_hybrid_ode.py
Tubular reactor	A PDE by the method of lines: a learned rate law in a 50-cell tube observed by four sensors.	uv run python examples/tubular_reactor/train_tubular_reactor.py
Batch reactor	Evosax search, then Optax refinement, on an Arrhenius trunk with a learned residual, compared against per-pH Arrhenius fits on held-out runs.	uv run python examples/batch_reactor/train_hybrid.py, then compare_baselines.py
Batch reactor RL	A bounded controller trained with PPO around a frozen hybrid model.	uv run python examples/batch_reactor/train_rl_deactivation.py
SBML hybrid kinetics	An external SBML mechanism with one rate law learned by a predictor.	uv run python examples/sbml_hybrid/train_sbml_hybrid.py
Neural polynomial kinetics	A structured NeuralNPolynomial rate law in place of a black-box MLP.	uv run python examples/supersaturation_poly/train_supersaturation_poly.py
Custom predictor	Writing a predictor family, freezing some of its arrays, and saving it.	uv run python examples/custom_predictor/train_custom_predictor.py
Custom training loop	A hand-written training loop built from the public gradient kernels.	uv run python examples/custom_loop/train_custom_loop.py
Mechanistic crystallisation	Four kinetic constants fitted with CMA-ES, no neural predictors.	uv run python examples/crystallisation/train_crystallisation_mechanistic.py

Read the harmonic oscillator first, then crystallisation for a full model on real data. Hybrid ODE covers where a network sits relative to the solver. The custom predictor and custom loop pages are for when the stock components no longer fit your model.