HeunSolver#

class deepinv.sampling.HeunSolver(timesteps=None, t_start=None, t_end=None, num_steps=None, rng=None)[source]#

Bases: BaseSDESolver

Heun solver for SDEs.

This solver uses the second-order Heun method to numerically integrate SDEs, defined as:

\[\begin{split}\tilde{x}_{t+dt} &= x_t + f(x_t,t)dt + g(t) W_{dt} \\ x_{t+dt} &= x_t + \frac{1}{2}[f(x_t,t) + f(\tilde{x}_{t+dt},t+dt)]dt + \frac{1}{2}[g(t) + g(t+dt)] W_{dt}\end{split}\]

where \(W_t\) is a Gaussian random variable with mean 0 and variance dt.

Parameters:

  • timesteps (torch.Tensor, numpy.ndarray, list) – The time steps at which to evaluate the solution.

  • timesteps – time steps at which the SDE will be discretized.

  • t_start (float) – the starting time of the SDE, optional. If not provided, it will be inferred from the timesteps argument.

  • t_end (float) – the ending time of the SDE, optional. If not provided, it will be inferred from the timesteps argument.

  • num_steps (int) – the number of time steps for the SDE, optional. If not provided, it will be inferred from the timesteps argument.

  • rng (torch.Generator) – A random number generator for reproducibility.

Note

You can either provide the timesteps argument directly, or specify t_start, t_end, and num_steps to generate the time steps automatically (linearly with constant stepsize). If both are provided, the timesteps argument will take precedence.