Examples Gallery

Each notebook below walks through a complete workflow on a benchmark system, but they are organised around package capabilities rather than the models themselves. Pick the one that matches what you want to do.

Notebooks¶

Four-Tank Hydraulic Network (Simultaneous)¶

A four-state, index-2 DAE with five algebraic flow variables. The NN replaces two nonlinear hydraulic relations. Demonstrates the end-to-end simultaneous workflow: defining a DAE ProblemDefinition, data generation, smoother, pre-training, training, and inference on new initial conditions.

Leslie-Gower Predator-Prey (Decomposition)¶

A two-state ODE trained with the decomposition approach. Demonstrates adding a custom path constraint (a Lyapunov descent inequality) to embed mechanistic prior knowledge during training.

Fed-Batch Bioreactor: Importing Measured Data¶

A four-state ODE with Monod growth kinetics. Demonstrates the bring-your-own-data workflow: loading measured time series from a CSV into obs_times / obs_values (no synthetic data generation), and verifying that the trained model produces physically feasible predictions under new operating conditions via inference.

Fed-Batch Bioreactor: Partial Observation¶

The same bioreactor, but only biomass and substrate are measured. Demonstrates the observation model (get_obs_vars with obs_dim smaller than the number of states), how to anchor unmeasured states with unfix_io=False, and reconstruction of the unmeasured product and volume.

Fed-Batch Bioreactor: Validation and Model Selection¶

Demonstrates leave-one-batch-out validation: holding out a batch, predicting it with inference, and sweeping the network width to choose the model that generalises best rather than the one that fits the training data hardest.

Command-line scripts¶

The same systems are available as runnable scripts in the examples/ directory, including a multi-trajectory MPI example:

# Single process
python examples/four_tank.py

# MPI (decomposition, 4 ranks)
mpirun -n 4 python examples/example_mpi.py

Set METHOD = 'simul' or METHOD = 'decomp' at the top of each script to switch between the two training algorithms.