BaseSDESolver

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

Bases: Module

Base class for solving Stochastic Differential Equations (SDEs) from deepinv.sampling.BaseSDE of the form:

\[d x_{t} = f(x_t, t) dt + g(t) d w_{t}\]

where \(f\) is the drift term, \(g\) is the diffusion coefficient, and \(w_t\) is a standard Brownian process.

Currently only supported for fixed time steps for numerical integration.

Parameters:

• timesteps (torch.Tensor, numpy.ndarray, list) – time steps at which the SDE will be discretized.e.

• rng (torch.Generator) – a random number generator for reproducibility, optional.

randn_like(input, seed=None)

Equivalent to torch.randn_like() but supports a pseudorandom number generator argument.

Parameters:

• input (torch.Tensor) – The input tensor whose size will be used.

• seed (int) – The seed for the random number generator, if rng is provided.

Returns:

A tensor of the same size as input filled with random numbers from a normal distribution.

Return type:

torch.Tensor

This method uses the rng attribute of the class, which is a pseudo-random number generator for reproducibility. If a seed is provided, it will be used to set the state of rng before generating the random numbers.

Note

The rng attribute must be initialized for this method to work properly.

reset_rng()

Reset the random number generator to its initial state.

rng_manual_seed(seed=None)

Sets the seed for the random number generator.

Parameters:

seed (int) – the seed to set for the random number generator. If not provided, the current state of the random number generator is used. Note: it will be ignored if the random number generator is not initialized.

sample(sde, x_init, seed=None, *args, timesteps=None, get_trajectory=False, **kwargs)

Solve the Stochastic Differential Equation (SDE) with given time steps.

This function iteratively applies the SDE solver step for each time interval defined by the provided timesteps.

Parameters:

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

• x_init (torch.Tensor) – The initial state of the system.

• seed (int) – The seed for the random number generator, if rng is provided.

• timesteps (torch.Tensor, numpy.ndarray, list) – A sequence of time points at which to solve the SDE. If None, default timesteps will be used.

• get_trajectory (bool) – whether to return the full trajectory of the SDE or only the last sample, optional. Default to False.

• *args – Variable length argument list to be passed to the step function.

• **kwargs – Arbitrary keyword arguments to be passed to the step function.

Returns:

SDEOutput

Return type:

SDEOutput

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

Examples using BaseSDESolver:

Posterior Sampling for Inverse Problems with Stochastic Differential Equations modeling.

Posterior Sampling for Inverse Problems with Stochastic Differential Equations modeling.