solve_ivp

xitorch.integrate.solve_ivp(fcn: Union[Callable[[…], torch.Tensor], Callable[[…], Sequence[torch.Tensor]]], ts: torch.Tensor, y0: torch.Tensor, params: Sequence[Any] = [], bck_options: Mapping[str, Any] = {}, method: Optional[Union[str, Callable]] = None, **fwd_options) → Union[torch.Tensor, Sequence[torch.Tensor]][source]

Solve the initial value problem (IVP) or also commonly known as ordinary differential equations (ODE), where given the initial value \(\mathbf{y_0}\), it then solves

\[\mathbf{y}(t) = \mathbf{y_0} + \int_{t_0}^{t} \mathbf{f}(t', \mathbf{y}, \theta)\ \mathrm{d}t'\]

Although the original solve_ivp does not accept batched ts, it can be batched using functorch’s vmap (only for explicit solver, though, e.g. rk38, rk4, and euler). Adaptive steps cannot be vmapped at the moment.

Parameters

  • fcn (callable) – The function that represents dy/dt. The function takes an input of a single time t and tensor y with shape (*ny) and produce \(\mathrm{d}\mathbf{y}/\mathrm{d}t\) with shape (*ny). The output of the function must be a tensor with shape (*ny) or a list of tensors.

  • ts (torch.tensor) – The time points where the value of y will be returned. It must be monotonically increasing or decreasing. It is a tensor with shape (nt,).

  • y0 (torch.tensor) – The initial value of y, i.e. y(t[0]) == y0. It is a tensor with shape (*ny) or a list of tensors.

  • params (list) – Sequence of other parameters required in the function.

  • bck_options (dict) – Options for the backward solve_ivp method. If not specified, it will take the same options as fwd_options.

  • method (str or callable or None) – Initial value problem solver. If None, it will choose "rk45".

  • **fwd_options – Method-specific option (see method section below).

Returns

The values of y for each time step in ts. It is a tensor with shape (nt,*ny) or a list of tensors

Return type

torch.tensor or a list of tensors

method="rk45"
solve_ivp(..., method="rk45", *, atol=1e-08, rtol=1e-05)

Perform the adaptive Runge-Kutta steps with order 4 and 5.

Keyword Arguments

  • atol (float) – The absolute error tolerance in deciding the steps

  • rtol (float) – The relative error tolerance in deciding the steps

method="rk23"
solve_ivp(..., method="rk23", *, atol=1e-08, rtol=1e-05)

Perform the adaptive Runge-Kutta steps with order 2 and 3.

Keyword Arguments

  • atol (float) – The absolute error tolerance in deciding the steps

  • rtol (float) – The relative error tolerance in deciding the steps

method="rk4"
solve_ivp(..., method="rk4")

Perform the Runge-Kutta steps of order 4 with a fixed step size.

method="rk38"
solve_ivp(..., method="rk38")
method="euler"
solve_ivp(..., method="euler")