Integration Models

Integration models perform numerical integration of derivative models while supporting automatic differentiation through time.

dynax.ODESolver

Integrate a function or submodule.

This class integrates \(\dot{y} = \text{func}(t, y, u, [\text{funcargs}])\) defined by a function or submodule func. The integration is performed using diffrax. This makes the ODESolver differentiable.

Example

>>> import jax.numpy as jnp
>>> from dynax import ODESolver
>>> def func(t, y, u):
...     return -y + u
>>> model = ODESolver(func)
>>> ts = jnp.linspace(0, 1, 100)
>>> y0 = jnp.array([0.5, 1.0, 2.0])
>>> us = jnp.sin(ts)  # Example input
>>> solution = model(ts, y0, us)
>>> print(solution.shape)
(100, 3)

__init__(func, augmentation=0, augmented_ic_learnable=False, solver=diffrax.Tsit5(), stepsize_controller=diffrax.PIDController(rtol=1e-06, atol=1e-06), max_steps=4096)

Initialize the ODESolver.

PARAMETER	DESCRIPTION
func	Function or submodel to integrate. The function arguments are (t, y, u, [funcargs]) with a scalar time t, a N-dimensional state vector y, a m-dimensional input vector u and an optional patree funcargs. The function must return an N-dimensional vector representing the state derivative. TYPE: Callable[..., Array]
augmentation	If augmentation is an array, it describes the vector of augmented states that are added to the inital state y0 before passing it to func. If augmentation is an integer, it describes how many extra dimensions are to be added to the state and initializes the augmented initial condition to all zeros. Defaults to 0. TYPE: int | Array DEFAULT: 0
augmented_ic_learnable	If True the initial condition of the augmented state is updated during training. Defaults to False. TYPE: bool DEFAULT: False
solver	Specifies the diffax solver to use for numerical integration. TYPE: diffrax.AbstractSolver DEFAULT: diffrax.Tsit5()
stepsize_controller	The diffrax stepsize controller to use for integration. TYPE: diffrax.AbstractStepSizeController DEFAULT: diffrax.PIDController(rtol=1e-06, atol=1e-06)
max_steps	The maximum number of steps to take before quitting the computation unconditionally. A value of None means no limit is imposed. TYPE: int | None DEFAULT: 4096

Note

The arguments solver, stepsize_controller, and max_steps are passed directly to the diffrax.diffeqsolve function. For more information view the diffrax documentation.

RAISES	DESCRIPTION
ValueError	If provided augmentation is neither an array or integer.

__call__(ts, y0, us=None, funcargs=None)

Solve ODE.

PARAMETER	DESCRIPTION
ts	Array of timesteps at which the solution is evaluated, with shape (k,). TYPE: Array
y0	Initial condition of the system state at time ts[0]. TYPE: Array
us	Two dimensional array of stacked input vectors at each timestep. Shape (k, m). Defaults to None. TYPE: Array | None DEFAULT: None
funcargs	Optional additional arguments to pass to the function func. TYPE: PyTree DEFAULT: None

RETURNS	DESCRIPTION
Array	Solution of the ODE excluding the augmented states. Shape (k, n).

get_augmented_trajectory(ts, y0, us=None, funcargs=None)

Return the ODE solution including the augmented states.

PARAMETER	DESCRIPTION
ts	Array of timesteps at which the solution is evaluated, with shape (k,). TYPE: Array
y0	Initial condition of the system state at time ts[0]. TYPE: Array
us	Two dimensional array of stacked input vectors at each timestep. Shape (k, m). Defaults to None. TYPE: Array | None DEFAULT: None
funcargs	Optional additional arguments to pass to the function func. TYPE: PyTree DEFAULT: None

RETURNS	DESCRIPTION
Array	Solution of the ODE including the augmented states. Shape (k, N).

get_solution(ts, y0, us=None, funcargs=None)

Return the diffrax.Solution object.

PARAMETER	DESCRIPTION
ts	Array of timesteps at which the solution is evaluated, with shape (k,). TYPE: Array
y0	Initial condition of the system state at time ts[0]. TYPE: Array
us	Two dimensional array of stacked input vectors at each timestep. Shape (k, m). Defaults to None. TYPE: Array | None DEFAULT: None
funcargs	Optional additional arguments to pass to the function func. TYPE: PyTree DEFAULT: None

RETURNS	DESCRIPTION
diffrax.Solution	diffrax solution object.