The AutoReduce Library

This chapter documents the public modules, classes, and functions that make up AutoReduce.

Systems

Core symbolic representation of nonlinear dynamical systems.

System

Class that stores the system model in this form: x_dot = f(x, theta), y = Cx.

Conversion from python-control input/output systems.

from_nonlinear_io_system

Create an AutoReduce System from a NonlinearIOSystem.

Conversion from PyDMD-style linear operators.

`from_linear_operator`	Create a `System` from a linear DMD operator matrix.
`from_dmd_model`	Create a `System` from a fitted PyDMD model.

Solvers

Numerical solvers for ordinary differential equation systems.

ODE

To solve the Model using scipy.odeint

Local sensitivity analysis solvers.

SSM

Class that computes local sensitivity analysis coefficients for the given Model using a numerical approximation method discussed in doi: https://doi.org/10.1016/0021-9991(76)90007-3 Uses numerical method to find sensitivity analysis matrix (SSM).

Reductions

Core reduction objects and shared reduction utilities.

`Reduce`	Working system used to build and compare reduced models.
`ReduceUtils`	Utility methods for reduction result objects.
`get_error_metric`	Compute the full-vs-reduced output error from systems.
`get_robustness_metric`	Compute robustness metrics from systems.
`create_system`	Create a base `System` from symbolic model data.

Time-scale separation reduction methods.

`solve_timescale_separation`	Solve a time-scale separation reduction for a system.
`explore_all_QSS_models`	Explore candidate QSS reductions for an autonomous system.
`reduce_with_input`	Compute candidate QSS reductions for systems with explicit inputs.

Symbolic helper functions for reduction algorithms.

`sympy_variables_exist`	Check whether variables appear in symbolic ODE expressions.
`sympy_solve_and_substitute`	Solve collapsed-state equations and substitute into ODEs.
`sympy_get_steady_state_solutions`	Solve each collapsed variable from its steady-state equation.

Conservation-law reduction methods.

`find_conserved_sets`	Find conserved species sets by summing ODE terms.
`setup_conservation_laws`	Create conservation-law expressions from conserved species sets.
`apply_conservation_laws`	Apply conservation laws to a system in place.
`solve_conservation_laws`	Find and apply conservation laws to a `System`.

Abundance-based model-reduction methods.

solve_approximations

Not implemented.

Projection-based reduced models using PyDMD.

`DMDReduction`	Fitted PyDMD model and the data used to construct it.
`fit_dmd`	Fit a dynamic mode decomposition model to state snapshots.
`fit_dmdc`	Fit a dynamic mode decomposition with control model.

Utilities

Model import and symbolic conversion utilities.

`load_ode_model`	Directly load an ODE skeleton with SymPy symbols.
`ode_to_sympy`	Returns Sympy object for the given ODE function
`sympy_to_sbml`	Return an SBML document for a SymPy-backed model.
`load_sbml`	Load an SBML file as a System object.

load_sbml(filename, outputs=None, rename_species=None, **kwargs) accepts an optional outputs argument naming one species or a list of species to preserve as linear outputs in the returned System. Output names must exactly match SBML species identifiers. If an output cannot be matched, load_sbml raises a ValueError listing the available species instead of failing with an internal lookup error.

The optional rename_species argument maps long SBML species identifiers to shorter SymPy symbol names for subsequent AutoReduce analysis.

Convenience functions for AutoReduce solvers.

`get_ODE`	Create an ODE solver for a system.
`solve_ODE_SSM`	Return state, output, and local sensitivity solutions.
`get_SSM`	Create an SSM solver for a system.
`solve_ode`	Solve a system over the given timepoints.
`solve_ssm`	Compute the local sensitivity matrix for a system.
`solve_sensitivity`	Solve the coupled state and local sensitivity equations.
`get_ode_solutions`	Solve a system over time and return transposed state trajectories.

SBML model construction utilities.

`create_sbml_model`	Creates an SBML Level 3 Version 2 model with some fixed standard settings.
`add_species`	Add species to SBML model
`add_reaction`	Add reaction to given model
`add_parameters`	Adds global parameters to the SBML Model