HeunSolver

class deepinv.sampling.HeunSolver(timesteps, rng=None)

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) – The time steps at which to evaluate the solution.

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

step(sde, t0, t1, x0, *args, **kwargs)

Perform a single step with step size from time t0 to time t1, with current state x0.

Parameters:

• sde (deepinv.sampling.BaseSDE) – the SDE to solve.

• t0 (float or torch.Tensor) – Time at the start of the step, of size (,).

• t1 (float or torch.Tensor) – Time at the end of the step, of size (,).

• x0 (torch.Tensor) – Current state of the system, of size (batch_size, d).

Returns:

Updated state of the system after the step.

Return type:

torch.Tensor